electrostatic force theory

8/17/2019 Electrostatic Force Theory

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Electrostatics or Static Electricity or FrictionalElectricity All of us have the experience of seeing a spark or hearing a cracklewhen we take o our synthetic clothes or sweater, particularly in dry

weather. The reason for these experiences is discharge of electriccharges through our body.

Static means anything that does not move or change with time.

The branch of physics, which deals with study of charges at rest (staticcharge), the force between the static charges elds and potentials dueto these charges is called as Electrostatics or Static Electricity.

Frictional Electricity is the electricity produced by rubbing twosuitable bodies and transfer of electrons fro one body to other.

!istorically, this phenonenon was discovered by a greek " Thales of #iletus" around $%%&'. The nae electricity was taken fro the reekword "lecktron".

What is Electric Charges

Charge is something possessed by material objects that makeit possible for them to exert electrical force and to respond toelectrical force.

There exists only two types of charges, naely positive andnegative. *ike charges repel and unlike charges attract eachother. 'harge is a scalar +uantity.

An electron attack another electron place c apart because of gravitational force with -.-x%$/ 0, whereas it observed anelectron repel another electron placed c apart because of electric

force is 2.3x102! 0. 1ince this repulsive force is very large ascopare to attractive force of gravitation, there ust besoe additional property associated with electron.


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"his additional property of electron# $hich gi%es rise to electricforce bet$een t$o electrons# is called as electric charge.

2hen a body gets the static charge by any eans then body is said to

be electri&ed or charged. 2hen it has no charge it is said tobe ne'tral.

3undaental Electronic Charge (e ) 1.* x 101+ C,. 14 unit

of charge is Coulomb ( C ) and is generally denoted by q.

-ote 5ecently, the existence of +uarks of charge 6 e and 7 e hasbeen postulated. 4f the +uarks are detected in any experient withconcrete practical evidence, then the iniu value of 8+uantu of charge9 will be either 6 e or 7 e. !owever, the law of +uantiation willhold good.

Two Kinds of Charges

4t was observed that if two glass rods rubbed with wool or silk cloth arebrought close to each other, they repel each other Fig. a. The twostrands of wool or two pieces of silk cloth, with which the rods wererubbed, also repel each other. !owever, the glass rod and wool

attracted each other.

1iilarly, two plastic rods rubbed with cat9s fur repelled eachother Fig. b but attracted the fur.:n the other hand, the plastic rods attract the glass rod Fig. c andrepel the silk or wool with which the glass rod is rubbed. The glass rodrepels the fur.

4f a plastic rod rubbed with fur is ade to touch two sall pith ballssuspended by silk or nylon thread, then the balls repel each otherFig.

d and are also repelled by the rod.

A siilar eect is found if the pith balls are touched with a glass rodrubbed with silk Fig. e.A draatic observation is that a pith ball touched with glass rodattracts another pith ball touched with plastic rod Fig. f .


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4t was concluded, that there are only two kinds of an entity whichis called the electric charge. The experients on pith ballssuggested that there are two kinds of electrication and we nd that

(i) like charges repel and(ii) ;nlike charges attract each other.

/y con%ention# the charge on glass rod or cats f'r is calledpositi%e and that on plastic rod or silk is termed negati%e.

The property which dierentiates the two kinds of charges is

called the polarity of charge.

-ote :nly rubbed area of non conducting body gets charged, and thischarge does not ove to other parts of the body. The charge is staticon rubbed portion only.

Conductors, Insulators and Dielectrics

Those substances which allow electricity to pass thro'gh them

easily are called cond'ctors. They have electric charges (electrons)that are coparatively free to ove inside the aterial.

#etals, huan and anial bodies and earth are conductors.

Those substances which do not allo$ electricity to pass thro'ghthem easily are called ins'lators.


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#ost of the nonetals like glass, porcelain, plastic, nylon, wood oerhigh resistance to the passage of electricity through the.

ns'lators are also called ielectric. :bviously, dielectric cannot

conduct electricity. !owever, when a electric &eld is applied#ind'ced charges appear on the s'rface of the dielectric. !encewe ay dene dielectric as the insulating aterial which transitselectric eects without conducting.

2hen we bring a charged body in contact with the earth, all the excesscharge on the body disappears by causing a oentary current topass to the ground through the connecting conductor (such as ourbody). This process of sharing the charges with the earth is calledgrounding or earthing.

Gold Leaf Electroscope

A siple apparatus to detect charge on a body is the goldleaf electroscope. 4t consists of a vertical etal rod housed in a box,with two thin gold leaves attached to its botto end.

2hen a charged ob


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The gold leaves are extreely thin conducting foils which havelow ass per unit area and are =exible, therefore, they respondvery +uickly to sall electrostatics forces.

This instruent can also be used check the polarity of charge

and to meas're the potential dierence.

asic !roperties of Charge

4f the si>es of charged bodies are very sall as copared to thedistances between the, we treat the as point charges. Allthe charge content of the body is assued to be concentrated atone point in space. 1oe other properties of the electric chargeare

1. 4dditi%e of charges 4f a systecontains n charges q, q?, q@, …, qn, then the total charge of thesyste is q + q? + q@ + … + qn .

'harge has agnitude but no direction. roper signs have to beused while adding the charges in a syste.

2. Charge is conser%ed 4t is not possible to create or destroy

net charge carried by any isolated syste. 1oeties nature creates charged particlesB a neutron turns intoa proton and an electron. The proton and electron thus createdhave e+ual and opposite charges and the total charge is >erobefore and after the creation.

3. 5'anti6ation of charge 'harges are integral ultiples of abasic unit of charge denoted by e. Thus charge + on a body isalways given by 7 ) ne. where n is any integer, positive or

negative. &y convention, the charge on an electron is taken to be negativeCtherefore charge on an electron is written as –e and that on aproton as +e. The fact that electric charge is always an integralultiple of e is tered as 7'anti6ation of charge.


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4n the 4nternational 1yste (14) of ;nits, a unit of charge iscalled a coulomb and is denoted by the sybol '.4n this syste,the value of the basic unit of charge is e = .$%?D? E %FD '.

Charging "y Induction

2hen we touch a pith ball with an electried plastic rod, soe of the negative charges on the rod are transferred to the pith balland it also gets charged. Thus the pith ball is charged by

contact. 4t is then repelled by the plastic rod but is attracted by aglass rod which is oppositely charged. The process of charging of body by contactGrubbing of body is called charging bycond'ction.

4n charging by ind'ction, a charged body A iparts to anotherbody &, soe charge of opposite sign without any contact

between A and &. The process o charging o body by withoutma!ing any contact with other o body is called charging by

induction. "ody # shall not lose any charge as it is not in contactwith ". Charging by induction is e$plained as below.

(i). "ring two metal spheres% # and "% supported on insulatingstands% in contact as shown in Fig. a.


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(ii) &ring a positively charged rod near one of the spheresC say A. The free electrons in the spheres are attracted towards the rod. This leaves an excess of positive charge on the rear surface of sphere &. &oth kinds of charges are resided on the surfaces, as

shown inFig. b.

The left surface of sphere A, has an excess of negative charge andthe right surface of sphere &, has an excess of positive charge.!owever, not all of the electrons in the spheres have accuulatedon the left surface of A.

As the negative charge starts building up at the left surface of A,other electrons are repelled by these. 4n a short tie, e+uilibriuis reached under the action of force of attraction of the rod andthe force of repulsion due to the accuulated charges.

"he process is called ind'ction of charge and happensalost instantly. The accuulated charges reain on the surface,as shown, till the glass rod is held near the sphere. 4f the rod isreoved, the charges are not acted by any outside force and theyredistribute to their original neutral state.

(iii) 1eparate the spheres by a sall distance while the glass rodis still held near sphere A, as shown in Fig. c. the two spheres arefound to be oppositely charged and attract each other.


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(iv)&emove the rod. The charges on spheres rearrange themselves as shown in Fig. d.

'ow% separate the spheres quite apart. The charges on them get uniormly distributedover them% as shown in Fig. e.

4n this process, the etal spheres will each be e+ual andoppositely charged.

-ote 4n the process of electric induction, the positively charged

glass rod does not lose any charge. This is contrary to charging byconduction, i.e. charging by actual contact where the charged

glass rod loses soe charge.

Co#parison of Charge $nd %ass

C849:E ;4SSlectric charge on the bodyay be positive or negative.

#ass of a body is a positive+uantity


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'harge carried by the bodydoes not depend upon thevelocity.

'harge carried by the bodydepends upon the velocity.

'harge is +uanti>ed #ass is not +uanti>ed yet.

lectric charge is alwaysconserved #ass can be changed intoenergy, it is not conserved.

3orce ay be attractive orrepulsive, according to thecharge

ravitational force betweentwo asses is alwaysattractive.

Coulo#"&s Law

Co'lomb meas'red the force bet$een t$o point charges

and fo'nd that it %aried in%ersely as the s7'are of thedistance bet$een the charges and $as directlyproportional to the prod'ct of the magnit'de of the t$ocharges and acted along the line joining the t$o charges.

Thus, if two point charges +, +? are separated by a distance r invacuu, the agnitude of the force (F) between the is given by

The choice of k deterines the si>e of the unit of charge. 4n 14units, the value of k is about D E %D. utting this value of k inabove +uation, we see that for q H q? H ', r H F H D E%D 0

"hat is# 1 C is the charge that $hen placed at a distance of 1 m from another charge of the same magnit'de in%ac''mexperiences an electrical force of rep'lsion of magnit'de + < 10+ -.

The constant k in is usually put as

or later convenience% so that Coulombs law is written as


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is called the Permittivity of free space .

The value of ermittivity of free space in 14 units is e+ual to I.I-JE %F? '? 0FF?

Dielectric Constant 'r (elati)e Electical !er#itti)ity

When the charges are isolated in medium other then vacuum, for is give

by

Where, ε is called absolute electrical Permittivity of medium. The

ratio which is given below is called relative electrical Permittivity of

medium.

The value of K depends only on the nature of medium.

Coulo#"&s Law In *ector For#

Let the position vectors of

charges q1 and q2 be r1 and r2 respectively Fig. We denote force on q1 due

to q2 by F12 and force on q2 due to q1 by F21. The two point

charges q1 and q2 have been numbered 1 and 2 for convenience and the

vector leading from 1 to 2 is denoted byr21


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r21 ! r2 " r1. #n the same way, the vector leading from 2 to 1 is denoted

by r12 r12 ! r1 " r2 ! " r21 .The magnitude of the vectors r21and r12 is

denoted by r 21 and r 12, respectively $r 12 ! r 21%. The direction of a vector isspecified by a unit vector along the vector. To denote the direction from

1 to 2 $or from 2 to 1%, we define the unit vectors

&oulomb's force law between two point charges q1 and q2 located

at r1 and r2 is then e(pressed as

#f q1 and q2 are of the same sign $either both positive and both

negative%, F21 is along )r 21, which denotes repulsion, as it should be for li*e charges. #f q1 and q2 are of opposite signs, F21 is along " )r 21$! )r 12%,

which denotes attraction, as e(pected for unli*e charges.

Thus, we do not have to write separate e+uations for the cases of li*e

and unli*e charges. €The force F12 on charge q1 due to charge q2, isobtained from force F21, by simply interchanging 1 and 2, i.e.

Thus, &oulomb's law agrees with the ewton's third law.

Continuous Charge Distri"ution

-n the surface of a charged conductor, it is impractical to specify the

charge distribution in terms of the locations of the microscopic charged


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constituents. #t is more feasible to consider an area element ∆S .On the

surface of the conductor $which is very small on the macroscopic scale

but big enough to include a very large number of electrons% and specify

the charge ∆Q on that element. We then define a surface charge

density σ at the area element by

We can do this at different points on the conductor and thus arrive at a

continuous function , called the surface charge density. The units

for σare &m2.

/imilar considerations apply for a line charge distribution and a volume

charge distribution. The linear charge density€

of a wire is defined

by

where ∆l is a small line element of wire on the macroscopic scale that,

however, includes a large number of microscopic charged constituents,

and ∆Q is the charge contained in that line element. The unit of linear

charge density $λ)€is &m.

The volume charge density $sometimes simply called charge density% isdefined in a similar manner


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where ∆Q is the charge included in the macroscopically small volume

element ∆V that includes a large number of microscopic charged

constituents. The unit for volume charge density ρ€is &m0.

Forces etween %ultiple Charges

&onsider a system of n stationary charges q1, q2, q0, ..., qn in

vacuum. orce on any charge due to a number of other charges is the

vector sum of all the forces on that charge due to the other charges,

ta*en one at a time. The individual forces are unaffected due to the

presence of other charges. This is termed as the principle of

superposition.

Consider a system of three charges q1, q2 and q0, as shown in Fig. Theforce on one charge, say q1, due to two other charges q2, q0 can therefore

be obtained by performing a vector addition of the forces due to each

one of these charges. Thus, if the force on q1 due to q2 is denoted

by F12, F12 is given by

#n the same way, the force on q1 due to q0, denoted by F10, is given by


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This again is the &oulomb force on q1 due to q0, even though other charge q2 is present.

Thus the total force F1 on q1 due to the two charges q2 and q0 is given as

The above calculation of force can be generalied to a system of charges

more than three, as shown in below ig.

The principle of superposition says that in a system of charges q1,q2, ...,

qn , the force on q1 due to q2 is the same as given by &oulomb's law, i.e.,

it is unaffected by the presence of the other charges q0, q3, ..., qn.

The total force F1 on the charge q1, due to all other charges, is then given

by the vector sum of the forces F12, F10, ..., F1n


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The vector sum is obtained as usual by the parallelogram law of addition

of vectors. 4ll of electrostatics is basically a conse+uence of &oulomb's

law and the superposition principle.

electrostatic force theory

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