![Page 1: Chapter IV: Electrostatic Field [5%] Electric Charge ...physics-eclass.weebly.com/uploads/1/6/2/2/16227420/...and_fields.pdf · Class XII Physics- Study Guide Prepared by Amit Dahal;](https://reader031.vdocuments.net/reader031/viewer/2022020104/5b219f737f8b9afa658b45e1/html5/thumbnails/1.jpg)
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 1 of 8
Chapter IV Electrostatic Field [5]
Electric Charge Electrostatics is the study of stationary electric charges - the study of electric fields produced by collections of
stationary charges A rod of plastic rubbed with fur or a rod of glass rubbed with silk will attract small pieces of
paper and is said to be electrically charged
When two charged [electrified] bodies of same charge are brought near to each other they repel each other Whereas
when bodies of opposite charge are brought near to each other they attract each other This explains the concept
that like charges repel and unlike charges attract each other
The nature of charge attracting or repelling another charge explains the fact that there exists a force between two
charges known as electrostatic force
Frictional Electricity When two objects are rubbed against each other electrons are transferred from one object to the other and acquires
attractive property In such cases objects are said to be electrified or charged with electricity
Electricity developed on objects when they are rubbed with each other is called Static electricity or Frictional
electricity
Since electrons are on the outer part of an atom electrification of a body is due to electrons only This is referred
to as Electron Theory of Electrification
Examples
a) When a glass rod is rubbed with silk cloth
Electrons from glass rod are transferred to the silk cloth
The glass rod acquires positive charge the silk cloth acquires negative charge
b) When a plastic rod is rubbed with fur
Electrons from the fur are transferred to the plastic rod
The fur acquires positive charge the plastic rod acquires negative charge
Conductors Semiconductors and Insulators
Conductors have more free electrons and the charge carriers are electrons while positive charge is
immobile
Semiconductors are materials whose conductivity can be increased by adding impurities Charge carriers
in them are either positive (holes) or negative (electrons)
Insulators do not have free electrons and cannot conduct electricity
SI Unit of charge
119868(119888119906119903119903119890119899119905) =119902(119888ℎ119886119903119892119890)
119905(119905119894119898119890)
there4 119902 = 119868119905
SI Unit of charge is Ampere seconds (As) called coulomb (C)
In electrostatics cgs system the unit of charge is known as electrostatic unit of charge (esu of charge)
It is also called statcoulomb (stat C)
1C = 3 x 109 stat C
In electromagnetic cgs system the unit of charge is known as electromagnetic unit of charge (emu of
charge)
1119862 =1
10119890119898 119906 119900119891 119886 119888ℎ119886119903119892119890
Other Units
microCoulomb (μC) 1 C = 106 μC
nanoCoulomb (nC) 1 C = 109 nC
Basic properties of electric charge
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 2 of 8
a) Additive Nature of Charge
The total electric charge on an object is equal to the algebraic sum of all the individual electric charges
distributed on the different parts of the object
If q1 q2 q3 hellip are electric charges present on different parts of an object then total electric charge on an
object is given by q = q1 + q2 + q3+hellip
b) Electric charge is Quantized
Quantization of charge states that the magnitude of charge on a body is an integral multiple of the magnitude
of charge of an electron
As per Millikanrsquos oil-drop experiment electric charges are the integral multiple of smallest amount of
charge This smallest amount is represented as e = 16 x 10-19C It cannot be divided indefinitely
The magnitude of the minimum charge a body can have is 16 x 10-19C Charge of any other magnitude
will always be an integral (1 2 3 4hellip) multiple of the charge on the electron
q = ne where n = plusmn0 plusmn1 plusmn2 plusmn3 hellip
Total charge (Q) = ne
c) Conservation of Charge
For an isolated system the net charge remains constant
Charges can neither be created nor be destroyed they can only be transferred from one part of the system
to the other
Examples
a) When silk is rubbed against the glass rod it is found that glass gets positively charged and silk gets negatively
charged The net charge in the silk-rod system remains zero both before and after rubbing
b) The production of a pair of a particle and its anti-particle (electron and positron) from a Υ-ray photon is called
pair production Pair production is conversion of energy to mass
120632 (ℎ119894119892ℎ119897119910 119890119899119890119903119892119890119905119894119888 119892119886119898119898119886 119903119886119910 119901ℎ119900119905119900119899) = 119942minus(119890119897119890119888119905119903119900119899) + 119942+(119901119900119904119894119905119903119900119899)
c) The conversion of a pair of particle and its anti-particle into invisible a Υ-ray photon is called pair annihilation
It shows wave nature of particle It is the production of energy form mass
119942minus(119890119897119890119888119905119903119900119899) + 119942+(119901119900119904119894119905119903119900119899) = 120632 + 120632
Coulombrsquos Law
It states that two stationary point charges lsquoq1rsquo and lsquoq2rsquo repel or attract each other with a force lsquoFrsquo which is
directly proportional to the products of the charges and inversely proportional to the square of the distance lsquorrsquo
between them
Coulombrsquos Law in Vector Form
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 3 of 8
Consider two positive point charges q1 and q2 placed in vacuum at a distance r from each other They repel each
other
Note Two charges situated at a certain distance apart exert maximum force on each other when they are
placed in vacuum (or air) In dielectric medium the force between them always decreases by a factor K
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 4 of 8
Electric Field The field or space around a charge particle where its force is experienced by any other charged particle is called
the electric field Electric field is also known as electrostatic field intensity
Electric Lines of Force If a free unit positive charge is placed in an electric field it will experience a force due to which the unit positive
charge will move along a particular path The path along which the unit positive charge will move due to
electrostatic force in the field is called electric lines of force
Properties of Electric Lines of Force or Field Lines
i The electric lines of force are imaginary lines
ii A unit positive charge placed in the electric field tends to follow a path along the field line if it is free to do so
iii The electric lines of force emanate from a positive charge and terminate on a negative charge
iv The tangent to an electric field line at any point gives the direction of the electric field at that point
v Two electric lines of force can never cross each other If they do then at the point of intersection there will
be two tangents It means there are two values of the electric field at that point which is not possible
Further electric field being a vector quantity there can be only one resultant field at the given
point represented by one tangent at the given point for the given line of force
vi Electric lines of force are closer (crowded) where the electric field is stronger and the lines spread out where
the electric field is weaker
vii Electric lines of force are perpendicular to the surface of a positively or negatively charged body
viii Electric lines of force contract lengthwise to represent attraction between two unlike charges
ix Electric lines of force exert lateral (sideways) pressure to represent repulsion between two like charges
x The number of lines per unit cross ndash sectional area perpendicular to the field lines (ie density of lines of force)
is directly proportional to the magnitude of the intensity of electric field in that region
xi Electric lines of force do not pass through a conductor Hence the interior of the conductor is free from the
influence of the electric field
xii Electric lines of force can pass through an insulator
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 5 of 8
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 6 of 8
Electric Field Intensity (E)
Electric intensity at a point is defined as the force experienced per unit positive charge at a point placed in an
electric field
=119865
1199020
SI unit is NC-1 or Vm-1
SI unit of electric field is NC-1 or Vm-1 (volts per meter)
Electric field due to a charge at a point is the force that a unit positive charge would experience if placed at
that point
The charge generating electric field is called source charge and the charge which experiences this field is
called test charge Practically to keep source charge undisturbed due to the electric field of test charge the
test charge is kept infinitely small
Since F (Force) is proportional to q (Charge) the electric field is independent of q but depends on r (space
coordinates)
From coulombrsquos law magnitude of force between two charges is given by
119865 =1
412058712057601199021199020
1199032
∵ 119864 =119865
1199020
there4 119864 =1
412058712057601199021199020
1199032divide 1199020
there4 119916 =120783
120786120645120634120782119954
119955120784
Electric potential
Electric potential is the amount of work done in moving a positive charge from one terminal to the other
This work done is stored as potential energy in the charge
119933 =119934
119954120782
Electric field strength in between the charged plates is related to electric potential as
119916 =119933
119941where 119837 is th distnce between the plates
From the above relation we can write electric potential as
119933 = 119916119941
Taking ldquodrdquo as ldquorrdquo we can re-write V = Ed as
119933 = 119916119955
there4 119933 =1
41205871205760119902
1199032times 119903 rArr 119933 =
120783
120786120645120634120782119954
119955
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 7 of 8
Motion of charged particle inside a uniform Electric field The motion of a charged particle in a uniform electric field is a projectile motion
When a charge q is placed in an electric field E the electric force on the charge is
F = Emiddotq
From Newtonrsquos second law F = m x a therefore m x a = E x q
The acceleration of the charge is
119938 =119916119954
119950
If the charge is positive the motion will be in the direction of the electric field
If the charge is negative the motion will be in the direction opposite the electric
field
The electric field in the region between two oppositely charged flat metal plates is considered to be uniform
If an electron is projected horizontally into an electric field with an initial velocity vo it will be accelerated by the
electric field
In the following situation the charges follow a parabolic path if moving perpendicular to the field
Flux of Vector Field The flux of a quantity is defined as the rate at which this quantity passes through a fixed boundary per unit time
Number of field lines crossing a particular area is proportional to vdA
Where
v = field vector dA = small area Ɵ = angle between the field vector and normal to the surface
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 8 of 8
Flux is found to be maximum when the area is in the same direction to that of the field vector (1049113 = 0o)
Flux is zero when the area is perpendicular to the field vector (1049113 = 90o)
Flux is a scalar quantity
Electric Flux (120509119916) Electric flux over an area in an electric field represents the total number of field lines crossing this area
The electric flux is the measure of number of lines of force passing through some surface held in the electric
field
Because electric field lines are drawn arbitrarily we quantify electric flux las 120509119916 = 119916119912 except that if the
surface is tilted fewer lines cut the surface
We define A to be a vector having a magnitude equal to the area of the surface in a direction normal to the
surface
The ldquoamount of surfacerdquo perpendicular to the electric field is A cos Ɵ
Therefore the amount of surface area effectively ldquocut throughrdquo by the electric field is A cos Ɵ
The direction of dA is normal to the surface
120509119916 is positive for leaving a surface and negative for entering a surface
SI unit of 120509119916
Φ119864 = EA cos Ɵ
Φ119864 = NC-1 m2
Φ119864 = Nm2C-1or Vm
Gaussrsquo Theorem
Gauss theorem states that the electric flux 120601119864through any closed surface is equal to 11205760 times the net charge lsquoqrsquo
enclosed by the surface
Φ119864 =119902
1205760
Where q enclosed charge and 120634120782 permittivity of free space
![Page 2: Chapter IV: Electrostatic Field [5%] Electric Charge ...physics-eclass.weebly.com/uploads/1/6/2/2/16227420/...and_fields.pdf · Class XII Physics- Study Guide Prepared by Amit Dahal;](https://reader031.vdocuments.net/reader031/viewer/2022020104/5b219f737f8b9afa658b45e1/html5/thumbnails/2.jpg)
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 2 of 8
a) Additive Nature of Charge
The total electric charge on an object is equal to the algebraic sum of all the individual electric charges
distributed on the different parts of the object
If q1 q2 q3 hellip are electric charges present on different parts of an object then total electric charge on an
object is given by q = q1 + q2 + q3+hellip
b) Electric charge is Quantized
Quantization of charge states that the magnitude of charge on a body is an integral multiple of the magnitude
of charge of an electron
As per Millikanrsquos oil-drop experiment electric charges are the integral multiple of smallest amount of
charge This smallest amount is represented as e = 16 x 10-19C It cannot be divided indefinitely
The magnitude of the minimum charge a body can have is 16 x 10-19C Charge of any other magnitude
will always be an integral (1 2 3 4hellip) multiple of the charge on the electron
q = ne where n = plusmn0 plusmn1 plusmn2 plusmn3 hellip
Total charge (Q) = ne
c) Conservation of Charge
For an isolated system the net charge remains constant
Charges can neither be created nor be destroyed they can only be transferred from one part of the system
to the other
Examples
a) When silk is rubbed against the glass rod it is found that glass gets positively charged and silk gets negatively
charged The net charge in the silk-rod system remains zero both before and after rubbing
b) The production of a pair of a particle and its anti-particle (electron and positron) from a Υ-ray photon is called
pair production Pair production is conversion of energy to mass
120632 (ℎ119894119892ℎ119897119910 119890119899119890119903119892119890119905119894119888 119892119886119898119898119886 119903119886119910 119901ℎ119900119905119900119899) = 119942minus(119890119897119890119888119905119903119900119899) + 119942+(119901119900119904119894119905119903119900119899)
c) The conversion of a pair of particle and its anti-particle into invisible a Υ-ray photon is called pair annihilation
It shows wave nature of particle It is the production of energy form mass
119942minus(119890119897119890119888119905119903119900119899) + 119942+(119901119900119904119894119905119903119900119899) = 120632 + 120632
Coulombrsquos Law
It states that two stationary point charges lsquoq1rsquo and lsquoq2rsquo repel or attract each other with a force lsquoFrsquo which is
directly proportional to the products of the charges and inversely proportional to the square of the distance lsquorrsquo
between them
Coulombrsquos Law in Vector Form
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 3 of 8
Consider two positive point charges q1 and q2 placed in vacuum at a distance r from each other They repel each
other
Note Two charges situated at a certain distance apart exert maximum force on each other when they are
placed in vacuum (or air) In dielectric medium the force between them always decreases by a factor K
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 4 of 8
Electric Field The field or space around a charge particle where its force is experienced by any other charged particle is called
the electric field Electric field is also known as electrostatic field intensity
Electric Lines of Force If a free unit positive charge is placed in an electric field it will experience a force due to which the unit positive
charge will move along a particular path The path along which the unit positive charge will move due to
electrostatic force in the field is called electric lines of force
Properties of Electric Lines of Force or Field Lines
i The electric lines of force are imaginary lines
ii A unit positive charge placed in the electric field tends to follow a path along the field line if it is free to do so
iii The electric lines of force emanate from a positive charge and terminate on a negative charge
iv The tangent to an electric field line at any point gives the direction of the electric field at that point
v Two electric lines of force can never cross each other If they do then at the point of intersection there will
be two tangents It means there are two values of the electric field at that point which is not possible
Further electric field being a vector quantity there can be only one resultant field at the given
point represented by one tangent at the given point for the given line of force
vi Electric lines of force are closer (crowded) where the electric field is stronger and the lines spread out where
the electric field is weaker
vii Electric lines of force are perpendicular to the surface of a positively or negatively charged body
viii Electric lines of force contract lengthwise to represent attraction between two unlike charges
ix Electric lines of force exert lateral (sideways) pressure to represent repulsion between two like charges
x The number of lines per unit cross ndash sectional area perpendicular to the field lines (ie density of lines of force)
is directly proportional to the magnitude of the intensity of electric field in that region
xi Electric lines of force do not pass through a conductor Hence the interior of the conductor is free from the
influence of the electric field
xii Electric lines of force can pass through an insulator
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 5 of 8
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 6 of 8
Electric Field Intensity (E)
Electric intensity at a point is defined as the force experienced per unit positive charge at a point placed in an
electric field
=119865
1199020
SI unit is NC-1 or Vm-1
SI unit of electric field is NC-1 or Vm-1 (volts per meter)
Electric field due to a charge at a point is the force that a unit positive charge would experience if placed at
that point
The charge generating electric field is called source charge and the charge which experiences this field is
called test charge Practically to keep source charge undisturbed due to the electric field of test charge the
test charge is kept infinitely small
Since F (Force) is proportional to q (Charge) the electric field is independent of q but depends on r (space
coordinates)
From coulombrsquos law magnitude of force between two charges is given by
119865 =1
412058712057601199021199020
1199032
∵ 119864 =119865
1199020
there4 119864 =1
412058712057601199021199020
1199032divide 1199020
there4 119916 =120783
120786120645120634120782119954
119955120784
Electric potential
Electric potential is the amount of work done in moving a positive charge from one terminal to the other
This work done is stored as potential energy in the charge
119933 =119934
119954120782
Electric field strength in between the charged plates is related to electric potential as
119916 =119933
119941where 119837 is th distnce between the plates
From the above relation we can write electric potential as
119933 = 119916119941
Taking ldquodrdquo as ldquorrdquo we can re-write V = Ed as
119933 = 119916119955
there4 119933 =1
41205871205760119902
1199032times 119903 rArr 119933 =
120783
120786120645120634120782119954
119955
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 7 of 8
Motion of charged particle inside a uniform Electric field The motion of a charged particle in a uniform electric field is a projectile motion
When a charge q is placed in an electric field E the electric force on the charge is
F = Emiddotq
From Newtonrsquos second law F = m x a therefore m x a = E x q
The acceleration of the charge is
119938 =119916119954
119950
If the charge is positive the motion will be in the direction of the electric field
If the charge is negative the motion will be in the direction opposite the electric
field
The electric field in the region between two oppositely charged flat metal plates is considered to be uniform
If an electron is projected horizontally into an electric field with an initial velocity vo it will be accelerated by the
electric field
In the following situation the charges follow a parabolic path if moving perpendicular to the field
Flux of Vector Field The flux of a quantity is defined as the rate at which this quantity passes through a fixed boundary per unit time
Number of field lines crossing a particular area is proportional to vdA
Where
v = field vector dA = small area Ɵ = angle between the field vector and normal to the surface
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 8 of 8
Flux is found to be maximum when the area is in the same direction to that of the field vector (1049113 = 0o)
Flux is zero when the area is perpendicular to the field vector (1049113 = 90o)
Flux is a scalar quantity
Electric Flux (120509119916) Electric flux over an area in an electric field represents the total number of field lines crossing this area
The electric flux is the measure of number of lines of force passing through some surface held in the electric
field
Because electric field lines are drawn arbitrarily we quantify electric flux las 120509119916 = 119916119912 except that if the
surface is tilted fewer lines cut the surface
We define A to be a vector having a magnitude equal to the area of the surface in a direction normal to the
surface
The ldquoamount of surfacerdquo perpendicular to the electric field is A cos Ɵ
Therefore the amount of surface area effectively ldquocut throughrdquo by the electric field is A cos Ɵ
The direction of dA is normal to the surface
120509119916 is positive for leaving a surface and negative for entering a surface
SI unit of 120509119916
Φ119864 = EA cos Ɵ
Φ119864 = NC-1 m2
Φ119864 = Nm2C-1or Vm
Gaussrsquo Theorem
Gauss theorem states that the electric flux 120601119864through any closed surface is equal to 11205760 times the net charge lsquoqrsquo
enclosed by the surface
Φ119864 =119902
1205760
Where q enclosed charge and 120634120782 permittivity of free space
![Page 3: Chapter IV: Electrostatic Field [5%] Electric Charge ...physics-eclass.weebly.com/uploads/1/6/2/2/16227420/...and_fields.pdf · Class XII Physics- Study Guide Prepared by Amit Dahal;](https://reader031.vdocuments.net/reader031/viewer/2022020104/5b219f737f8b9afa658b45e1/html5/thumbnails/3.jpg)
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 3 of 8
Consider two positive point charges q1 and q2 placed in vacuum at a distance r from each other They repel each
other
Note Two charges situated at a certain distance apart exert maximum force on each other when they are
placed in vacuum (or air) In dielectric medium the force between them always decreases by a factor K
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 4 of 8
Electric Field The field or space around a charge particle where its force is experienced by any other charged particle is called
the electric field Electric field is also known as electrostatic field intensity
Electric Lines of Force If a free unit positive charge is placed in an electric field it will experience a force due to which the unit positive
charge will move along a particular path The path along which the unit positive charge will move due to
electrostatic force in the field is called electric lines of force
Properties of Electric Lines of Force or Field Lines
i The electric lines of force are imaginary lines
ii A unit positive charge placed in the electric field tends to follow a path along the field line if it is free to do so
iii The electric lines of force emanate from a positive charge and terminate on a negative charge
iv The tangent to an electric field line at any point gives the direction of the electric field at that point
v Two electric lines of force can never cross each other If they do then at the point of intersection there will
be two tangents It means there are two values of the electric field at that point which is not possible
Further electric field being a vector quantity there can be only one resultant field at the given
point represented by one tangent at the given point for the given line of force
vi Electric lines of force are closer (crowded) where the electric field is stronger and the lines spread out where
the electric field is weaker
vii Electric lines of force are perpendicular to the surface of a positively or negatively charged body
viii Electric lines of force contract lengthwise to represent attraction between two unlike charges
ix Electric lines of force exert lateral (sideways) pressure to represent repulsion between two like charges
x The number of lines per unit cross ndash sectional area perpendicular to the field lines (ie density of lines of force)
is directly proportional to the magnitude of the intensity of electric field in that region
xi Electric lines of force do not pass through a conductor Hence the interior of the conductor is free from the
influence of the electric field
xii Electric lines of force can pass through an insulator
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 5 of 8
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 6 of 8
Electric Field Intensity (E)
Electric intensity at a point is defined as the force experienced per unit positive charge at a point placed in an
electric field
=119865
1199020
SI unit is NC-1 or Vm-1
SI unit of electric field is NC-1 or Vm-1 (volts per meter)
Electric field due to a charge at a point is the force that a unit positive charge would experience if placed at
that point
The charge generating electric field is called source charge and the charge which experiences this field is
called test charge Practically to keep source charge undisturbed due to the electric field of test charge the
test charge is kept infinitely small
Since F (Force) is proportional to q (Charge) the electric field is independent of q but depends on r (space
coordinates)
From coulombrsquos law magnitude of force between two charges is given by
119865 =1
412058712057601199021199020
1199032
∵ 119864 =119865
1199020
there4 119864 =1
412058712057601199021199020
1199032divide 1199020
there4 119916 =120783
120786120645120634120782119954
119955120784
Electric potential
Electric potential is the amount of work done in moving a positive charge from one terminal to the other
This work done is stored as potential energy in the charge
119933 =119934
119954120782
Electric field strength in between the charged plates is related to electric potential as
119916 =119933
119941where 119837 is th distnce between the plates
From the above relation we can write electric potential as
119933 = 119916119941
Taking ldquodrdquo as ldquorrdquo we can re-write V = Ed as
119933 = 119916119955
there4 119933 =1
41205871205760119902
1199032times 119903 rArr 119933 =
120783
120786120645120634120782119954
119955
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 7 of 8
Motion of charged particle inside a uniform Electric field The motion of a charged particle in a uniform electric field is a projectile motion
When a charge q is placed in an electric field E the electric force on the charge is
F = Emiddotq
From Newtonrsquos second law F = m x a therefore m x a = E x q
The acceleration of the charge is
119938 =119916119954
119950
If the charge is positive the motion will be in the direction of the electric field
If the charge is negative the motion will be in the direction opposite the electric
field
The electric field in the region between two oppositely charged flat metal plates is considered to be uniform
If an electron is projected horizontally into an electric field with an initial velocity vo it will be accelerated by the
electric field
In the following situation the charges follow a parabolic path if moving perpendicular to the field
Flux of Vector Field The flux of a quantity is defined as the rate at which this quantity passes through a fixed boundary per unit time
Number of field lines crossing a particular area is proportional to vdA
Where
v = field vector dA = small area Ɵ = angle between the field vector and normal to the surface
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 8 of 8
Flux is found to be maximum when the area is in the same direction to that of the field vector (1049113 = 0o)
Flux is zero when the area is perpendicular to the field vector (1049113 = 90o)
Flux is a scalar quantity
Electric Flux (120509119916) Electric flux over an area in an electric field represents the total number of field lines crossing this area
The electric flux is the measure of number of lines of force passing through some surface held in the electric
field
Because electric field lines are drawn arbitrarily we quantify electric flux las 120509119916 = 119916119912 except that if the
surface is tilted fewer lines cut the surface
We define A to be a vector having a magnitude equal to the area of the surface in a direction normal to the
surface
The ldquoamount of surfacerdquo perpendicular to the electric field is A cos Ɵ
Therefore the amount of surface area effectively ldquocut throughrdquo by the electric field is A cos Ɵ
The direction of dA is normal to the surface
120509119916 is positive for leaving a surface and negative for entering a surface
SI unit of 120509119916
Φ119864 = EA cos Ɵ
Φ119864 = NC-1 m2
Φ119864 = Nm2C-1or Vm
Gaussrsquo Theorem
Gauss theorem states that the electric flux 120601119864through any closed surface is equal to 11205760 times the net charge lsquoqrsquo
enclosed by the surface
Φ119864 =119902
1205760
Where q enclosed charge and 120634120782 permittivity of free space
![Page 4: Chapter IV: Electrostatic Field [5%] Electric Charge ...physics-eclass.weebly.com/uploads/1/6/2/2/16227420/...and_fields.pdf · Class XII Physics- Study Guide Prepared by Amit Dahal;](https://reader031.vdocuments.net/reader031/viewer/2022020104/5b219f737f8b9afa658b45e1/html5/thumbnails/4.jpg)
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 4 of 8
Electric Field The field or space around a charge particle where its force is experienced by any other charged particle is called
the electric field Electric field is also known as electrostatic field intensity
Electric Lines of Force If a free unit positive charge is placed in an electric field it will experience a force due to which the unit positive
charge will move along a particular path The path along which the unit positive charge will move due to
electrostatic force in the field is called electric lines of force
Properties of Electric Lines of Force or Field Lines
i The electric lines of force are imaginary lines
ii A unit positive charge placed in the electric field tends to follow a path along the field line if it is free to do so
iii The electric lines of force emanate from a positive charge and terminate on a negative charge
iv The tangent to an electric field line at any point gives the direction of the electric field at that point
v Two electric lines of force can never cross each other If they do then at the point of intersection there will
be two tangents It means there are two values of the electric field at that point which is not possible
Further electric field being a vector quantity there can be only one resultant field at the given
point represented by one tangent at the given point for the given line of force
vi Electric lines of force are closer (crowded) where the electric field is stronger and the lines spread out where
the electric field is weaker
vii Electric lines of force are perpendicular to the surface of a positively or negatively charged body
viii Electric lines of force contract lengthwise to represent attraction between two unlike charges
ix Electric lines of force exert lateral (sideways) pressure to represent repulsion between two like charges
x The number of lines per unit cross ndash sectional area perpendicular to the field lines (ie density of lines of force)
is directly proportional to the magnitude of the intensity of electric field in that region
xi Electric lines of force do not pass through a conductor Hence the interior of the conductor is free from the
influence of the electric field
xii Electric lines of force can pass through an insulator
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 5 of 8
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 6 of 8
Electric Field Intensity (E)
Electric intensity at a point is defined as the force experienced per unit positive charge at a point placed in an
electric field
=119865
1199020
SI unit is NC-1 or Vm-1
SI unit of electric field is NC-1 or Vm-1 (volts per meter)
Electric field due to a charge at a point is the force that a unit positive charge would experience if placed at
that point
The charge generating electric field is called source charge and the charge which experiences this field is
called test charge Practically to keep source charge undisturbed due to the electric field of test charge the
test charge is kept infinitely small
Since F (Force) is proportional to q (Charge) the electric field is independent of q but depends on r (space
coordinates)
From coulombrsquos law magnitude of force between two charges is given by
119865 =1
412058712057601199021199020
1199032
∵ 119864 =119865
1199020
there4 119864 =1
412058712057601199021199020
1199032divide 1199020
there4 119916 =120783
120786120645120634120782119954
119955120784
Electric potential
Electric potential is the amount of work done in moving a positive charge from one terminal to the other
This work done is stored as potential energy in the charge
119933 =119934
119954120782
Electric field strength in between the charged plates is related to electric potential as
119916 =119933
119941where 119837 is th distnce between the plates
From the above relation we can write electric potential as
119933 = 119916119941
Taking ldquodrdquo as ldquorrdquo we can re-write V = Ed as
119933 = 119916119955
there4 119933 =1
41205871205760119902
1199032times 119903 rArr 119933 =
120783
120786120645120634120782119954
119955
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 7 of 8
Motion of charged particle inside a uniform Electric field The motion of a charged particle in a uniform electric field is a projectile motion
When a charge q is placed in an electric field E the electric force on the charge is
F = Emiddotq
From Newtonrsquos second law F = m x a therefore m x a = E x q
The acceleration of the charge is
119938 =119916119954
119950
If the charge is positive the motion will be in the direction of the electric field
If the charge is negative the motion will be in the direction opposite the electric
field
The electric field in the region between two oppositely charged flat metal plates is considered to be uniform
If an electron is projected horizontally into an electric field with an initial velocity vo it will be accelerated by the
electric field
In the following situation the charges follow a parabolic path if moving perpendicular to the field
Flux of Vector Field The flux of a quantity is defined as the rate at which this quantity passes through a fixed boundary per unit time
Number of field lines crossing a particular area is proportional to vdA
Where
v = field vector dA = small area Ɵ = angle between the field vector and normal to the surface
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 8 of 8
Flux is found to be maximum when the area is in the same direction to that of the field vector (1049113 = 0o)
Flux is zero when the area is perpendicular to the field vector (1049113 = 90o)
Flux is a scalar quantity
Electric Flux (120509119916) Electric flux over an area in an electric field represents the total number of field lines crossing this area
The electric flux is the measure of number of lines of force passing through some surface held in the electric
field
Because electric field lines are drawn arbitrarily we quantify electric flux las 120509119916 = 119916119912 except that if the
surface is tilted fewer lines cut the surface
We define A to be a vector having a magnitude equal to the area of the surface in a direction normal to the
surface
The ldquoamount of surfacerdquo perpendicular to the electric field is A cos Ɵ
Therefore the amount of surface area effectively ldquocut throughrdquo by the electric field is A cos Ɵ
The direction of dA is normal to the surface
120509119916 is positive for leaving a surface and negative for entering a surface
SI unit of 120509119916
Φ119864 = EA cos Ɵ
Φ119864 = NC-1 m2
Φ119864 = Nm2C-1or Vm
Gaussrsquo Theorem
Gauss theorem states that the electric flux 120601119864through any closed surface is equal to 11205760 times the net charge lsquoqrsquo
enclosed by the surface
Φ119864 =119902
1205760
Where q enclosed charge and 120634120782 permittivity of free space
![Page 5: Chapter IV: Electrostatic Field [5%] Electric Charge ...physics-eclass.weebly.com/uploads/1/6/2/2/16227420/...and_fields.pdf · Class XII Physics- Study Guide Prepared by Amit Dahal;](https://reader031.vdocuments.net/reader031/viewer/2022020104/5b219f737f8b9afa658b45e1/html5/thumbnails/5.jpg)
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 5 of 8
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 6 of 8
Electric Field Intensity (E)
Electric intensity at a point is defined as the force experienced per unit positive charge at a point placed in an
electric field
=119865
1199020
SI unit is NC-1 or Vm-1
SI unit of electric field is NC-1 or Vm-1 (volts per meter)
Electric field due to a charge at a point is the force that a unit positive charge would experience if placed at
that point
The charge generating electric field is called source charge and the charge which experiences this field is
called test charge Practically to keep source charge undisturbed due to the electric field of test charge the
test charge is kept infinitely small
Since F (Force) is proportional to q (Charge) the electric field is independent of q but depends on r (space
coordinates)
From coulombrsquos law magnitude of force between two charges is given by
119865 =1
412058712057601199021199020
1199032
∵ 119864 =119865
1199020
there4 119864 =1
412058712057601199021199020
1199032divide 1199020
there4 119916 =120783
120786120645120634120782119954
119955120784
Electric potential
Electric potential is the amount of work done in moving a positive charge from one terminal to the other
This work done is stored as potential energy in the charge
119933 =119934
119954120782
Electric field strength in between the charged plates is related to electric potential as
119916 =119933
119941where 119837 is th distnce between the plates
From the above relation we can write electric potential as
119933 = 119916119941
Taking ldquodrdquo as ldquorrdquo we can re-write V = Ed as
119933 = 119916119955
there4 119933 =1
41205871205760119902
1199032times 119903 rArr 119933 =
120783
120786120645120634120782119954
119955
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 7 of 8
Motion of charged particle inside a uniform Electric field The motion of a charged particle in a uniform electric field is a projectile motion
When a charge q is placed in an electric field E the electric force on the charge is
F = Emiddotq
From Newtonrsquos second law F = m x a therefore m x a = E x q
The acceleration of the charge is
119938 =119916119954
119950
If the charge is positive the motion will be in the direction of the electric field
If the charge is negative the motion will be in the direction opposite the electric
field
The electric field in the region between two oppositely charged flat metal plates is considered to be uniform
If an electron is projected horizontally into an electric field with an initial velocity vo it will be accelerated by the
electric field
In the following situation the charges follow a parabolic path if moving perpendicular to the field
Flux of Vector Field The flux of a quantity is defined as the rate at which this quantity passes through a fixed boundary per unit time
Number of field lines crossing a particular area is proportional to vdA
Where
v = field vector dA = small area Ɵ = angle between the field vector and normal to the surface
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 8 of 8
Flux is found to be maximum when the area is in the same direction to that of the field vector (1049113 = 0o)
Flux is zero when the area is perpendicular to the field vector (1049113 = 90o)
Flux is a scalar quantity
Electric Flux (120509119916) Electric flux over an area in an electric field represents the total number of field lines crossing this area
The electric flux is the measure of number of lines of force passing through some surface held in the electric
field
Because electric field lines are drawn arbitrarily we quantify electric flux las 120509119916 = 119916119912 except that if the
surface is tilted fewer lines cut the surface
We define A to be a vector having a magnitude equal to the area of the surface in a direction normal to the
surface
The ldquoamount of surfacerdquo perpendicular to the electric field is A cos Ɵ
Therefore the amount of surface area effectively ldquocut throughrdquo by the electric field is A cos Ɵ
The direction of dA is normal to the surface
120509119916 is positive for leaving a surface and negative for entering a surface
SI unit of 120509119916
Φ119864 = EA cos Ɵ
Φ119864 = NC-1 m2
Φ119864 = Nm2C-1or Vm
Gaussrsquo Theorem
Gauss theorem states that the electric flux 120601119864through any closed surface is equal to 11205760 times the net charge lsquoqrsquo
enclosed by the surface
Φ119864 =119902
1205760
Where q enclosed charge and 120634120782 permittivity of free space
![Page 6: Chapter IV: Electrostatic Field [5%] Electric Charge ...physics-eclass.weebly.com/uploads/1/6/2/2/16227420/...and_fields.pdf · Class XII Physics- Study Guide Prepared by Amit Dahal;](https://reader031.vdocuments.net/reader031/viewer/2022020104/5b219f737f8b9afa658b45e1/html5/thumbnails/6.jpg)
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 6 of 8
Electric Field Intensity (E)
Electric intensity at a point is defined as the force experienced per unit positive charge at a point placed in an
electric field
=119865
1199020
SI unit is NC-1 or Vm-1
SI unit of electric field is NC-1 or Vm-1 (volts per meter)
Electric field due to a charge at a point is the force that a unit positive charge would experience if placed at
that point
The charge generating electric field is called source charge and the charge which experiences this field is
called test charge Practically to keep source charge undisturbed due to the electric field of test charge the
test charge is kept infinitely small
Since F (Force) is proportional to q (Charge) the electric field is independent of q but depends on r (space
coordinates)
From coulombrsquos law magnitude of force between two charges is given by
119865 =1
412058712057601199021199020
1199032
∵ 119864 =119865
1199020
there4 119864 =1
412058712057601199021199020
1199032divide 1199020
there4 119916 =120783
120786120645120634120782119954
119955120784
Electric potential
Electric potential is the amount of work done in moving a positive charge from one terminal to the other
This work done is stored as potential energy in the charge
119933 =119934
119954120782
Electric field strength in between the charged plates is related to electric potential as
119916 =119933
119941where 119837 is th distnce between the plates
From the above relation we can write electric potential as
119933 = 119916119941
Taking ldquodrdquo as ldquorrdquo we can re-write V = Ed as
119933 = 119916119955
there4 119933 =1
41205871205760119902
1199032times 119903 rArr 119933 =
120783
120786120645120634120782119954
119955
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 7 of 8
Motion of charged particle inside a uniform Electric field The motion of a charged particle in a uniform electric field is a projectile motion
When a charge q is placed in an electric field E the electric force on the charge is
F = Emiddotq
From Newtonrsquos second law F = m x a therefore m x a = E x q
The acceleration of the charge is
119938 =119916119954
119950
If the charge is positive the motion will be in the direction of the electric field
If the charge is negative the motion will be in the direction opposite the electric
field
The electric field in the region between two oppositely charged flat metal plates is considered to be uniform
If an electron is projected horizontally into an electric field with an initial velocity vo it will be accelerated by the
electric field
In the following situation the charges follow a parabolic path if moving perpendicular to the field
Flux of Vector Field The flux of a quantity is defined as the rate at which this quantity passes through a fixed boundary per unit time
Number of field lines crossing a particular area is proportional to vdA
Where
v = field vector dA = small area Ɵ = angle between the field vector and normal to the surface
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 8 of 8
Flux is found to be maximum when the area is in the same direction to that of the field vector (1049113 = 0o)
Flux is zero when the area is perpendicular to the field vector (1049113 = 90o)
Flux is a scalar quantity
Electric Flux (120509119916) Electric flux over an area in an electric field represents the total number of field lines crossing this area
The electric flux is the measure of number of lines of force passing through some surface held in the electric
field
Because electric field lines are drawn arbitrarily we quantify electric flux las 120509119916 = 119916119912 except that if the
surface is tilted fewer lines cut the surface
We define A to be a vector having a magnitude equal to the area of the surface in a direction normal to the
surface
The ldquoamount of surfacerdquo perpendicular to the electric field is A cos Ɵ
Therefore the amount of surface area effectively ldquocut throughrdquo by the electric field is A cos Ɵ
The direction of dA is normal to the surface
120509119916 is positive for leaving a surface and negative for entering a surface
SI unit of 120509119916
Φ119864 = EA cos Ɵ
Φ119864 = NC-1 m2
Φ119864 = Nm2C-1or Vm
Gaussrsquo Theorem
Gauss theorem states that the electric flux 120601119864through any closed surface is equal to 11205760 times the net charge lsquoqrsquo
enclosed by the surface
Φ119864 =119902
1205760
Where q enclosed charge and 120634120782 permittivity of free space
![Page 7: Chapter IV: Electrostatic Field [5%] Electric Charge ...physics-eclass.weebly.com/uploads/1/6/2/2/16227420/...and_fields.pdf · Class XII Physics- Study Guide Prepared by Amit Dahal;](https://reader031.vdocuments.net/reader031/viewer/2022020104/5b219f737f8b9afa658b45e1/html5/thumbnails/7.jpg)
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 7 of 8
Motion of charged particle inside a uniform Electric field The motion of a charged particle in a uniform electric field is a projectile motion
When a charge q is placed in an electric field E the electric force on the charge is
F = Emiddotq
From Newtonrsquos second law F = m x a therefore m x a = E x q
The acceleration of the charge is
119938 =119916119954
119950
If the charge is positive the motion will be in the direction of the electric field
If the charge is negative the motion will be in the direction opposite the electric
field
The electric field in the region between two oppositely charged flat metal plates is considered to be uniform
If an electron is projected horizontally into an electric field with an initial velocity vo it will be accelerated by the
electric field
In the following situation the charges follow a parabolic path if moving perpendicular to the field
Flux of Vector Field The flux of a quantity is defined as the rate at which this quantity passes through a fixed boundary per unit time
Number of field lines crossing a particular area is proportional to vdA
Where
v = field vector dA = small area Ɵ = angle between the field vector and normal to the surface
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 8 of 8
Flux is found to be maximum when the area is in the same direction to that of the field vector (1049113 = 0o)
Flux is zero when the area is perpendicular to the field vector (1049113 = 90o)
Flux is a scalar quantity
Electric Flux (120509119916) Electric flux over an area in an electric field represents the total number of field lines crossing this area
The electric flux is the measure of number of lines of force passing through some surface held in the electric
field
Because electric field lines are drawn arbitrarily we quantify electric flux las 120509119916 = 119916119912 except that if the
surface is tilted fewer lines cut the surface
We define A to be a vector having a magnitude equal to the area of the surface in a direction normal to the
surface
The ldquoamount of surfacerdquo perpendicular to the electric field is A cos Ɵ
Therefore the amount of surface area effectively ldquocut throughrdquo by the electric field is A cos Ɵ
The direction of dA is normal to the surface
120509119916 is positive for leaving a surface and negative for entering a surface
SI unit of 120509119916
Φ119864 = EA cos Ɵ
Φ119864 = NC-1 m2
Φ119864 = Nm2C-1or Vm
Gaussrsquo Theorem
Gauss theorem states that the electric flux 120601119864through any closed surface is equal to 11205760 times the net charge lsquoqrsquo
enclosed by the surface
Φ119864 =119902
1205760
Where q enclosed charge and 120634120782 permittivity of free space
![Page 8: Chapter IV: Electrostatic Field [5%] Electric Charge ...physics-eclass.weebly.com/uploads/1/6/2/2/16227420/...and_fields.pdf · Class XII Physics- Study Guide Prepared by Amit Dahal;](https://reader031.vdocuments.net/reader031/viewer/2022020104/5b219f737f8b9afa658b45e1/html5/thumbnails/8.jpg)
Class XII Physics- Study Guide
Prepared by Amit Dahal YHSS Page 8 of 8
Flux is found to be maximum when the area is in the same direction to that of the field vector (1049113 = 0o)
Flux is zero when the area is perpendicular to the field vector (1049113 = 90o)
Flux is a scalar quantity
Electric Flux (120509119916) Electric flux over an area in an electric field represents the total number of field lines crossing this area
The electric flux is the measure of number of lines of force passing through some surface held in the electric
field
Because electric field lines are drawn arbitrarily we quantify electric flux las 120509119916 = 119916119912 except that if the
surface is tilted fewer lines cut the surface
We define A to be a vector having a magnitude equal to the area of the surface in a direction normal to the
surface
The ldquoamount of surfacerdquo perpendicular to the electric field is A cos Ɵ
Therefore the amount of surface area effectively ldquocut throughrdquo by the electric field is A cos Ɵ
The direction of dA is normal to the surface
120509119916 is positive for leaving a surface and negative for entering a surface
SI unit of 120509119916
Φ119864 = EA cos Ɵ
Φ119864 = NC-1 m2
Φ119864 = Nm2C-1or Vm
Gaussrsquo Theorem
Gauss theorem states that the electric flux 120601119864through any closed surface is equal to 11205760 times the net charge lsquoqrsquo
enclosed by the surface
Φ119864 =119902
1205760
Where q enclosed charge and 120634120782 permittivity of free space
