george cross electromagnetism electric field lecture27 (2)
DESCRIPTION
Electric field, field of multiple charges, field of continuous charge, parallel plate capacitor, motion of charge in electric field, motion of dipole in fieldTRANSCRIPT
Antelope Valley CollegeMath & Sciences Dept
George Cross
General PhysicsPhysics 120
Chapter 27: THE ELECTRICFIELD
TODAYS LECTURE
• THE ELECTRIC FIELD– Electric Field Models– The Electric Field of Multiple Point Charges– The Electric Field of a Continuous Charge
Distribution– The Electric Fields of Rings, Disks, Planes,
and Spheres– The Parallel-Plate Capacitor– Motion of a Charged Particle in an Electric
Field– Motion of a Dipole in an Electric Field
CHAPTER 27 QUIZ
1. Which statement/s is/are not true?• The electric field obeys the principle of superposition.• The tangent to an electric field line at a point gives the
direction of the field at that point.• The density of electric field lines is directly proportional to
the strength of the field.• Negative charges are sources of electric field lines and
positive charges are sinks of electric field lines.• Electric fields are what you find in PlayStation football
and soccer games.
CHAPTER 27 QUIZ
2. An electric dipole in a uniform electric field experiences
• Happiness and excitement• only a net external force.• only a torque.• both a net external force and a torque.• neither a net external force nor a torque.• answer depends on the strength of the field
3. Choose the correct statement/s concerning electric field lines: a.) field lines may cross
b). field lines are close together where the field is large
c). field lines point away from negative charge
d). a point charge released from rest moves along a field line
e). field lines are made with white chalk
f). none of these are correct
4. What device provides a practical way to produce a uniform electric field?
a). A Cathodic Ray Tubeb). An Infinite line of chargec). An infinite sheet of charged). A parallel plate capacitore). X-Boxf). A battery
5. Which of these charge distributions did not have its electric field calculated in detail in Chapter 27?
a. A line of charge. .
b. A ring of charge. .
c. A plane of charge
d. A parallel-plate capacitor
e. They were all calculated
CHAPTER 27 QUIZ
1. Which statement/s is/are not true?• The electric field obeys the principle of superposition.• The tangent to an electric field line at a point gives the
direction of the field at that point.• The density of electric field lines is directly proportional to
the strength of the field.• Negative charges are sources of electric field lines and
positive charges are sinks of electric field lines.• Electric fields are what you find in PlayStation football
and soccer games.
CHAPTER 27 QUIZ
2. An electric dipole in a uniform electric field experiences
• Happiness and excitement• only a net external force.• only a torque.• both a net external force and a torque.• neither a net external force nor a torque.• answer depends on the strength of the field
3. Choose the correct statement/s concerning electric field lines: a.) field lines may cross
b). field lines are close together where the field is large
c). field lines point away from negative charge
d). a point charge released from rest moves along a field line
e). field lines are made with white chalk
f). none of these are correct
4. What device provides a practical way to produce a uniform electric field?
a). A Cathodic Ray Tubeb). An Infinite line of chargec). An infinite sheet of charged). A parallel plate capacitore). X-Boxf). A battery
5. Which of these charge distributions did not have its electric field calculated in detail in Chapter 27?
a. A line of charge. .
b. A ring of charge. .
c. A plane of charge
d. A parallel-plate capacitor
e. They were all calculated
Electric Field Models
We can understand much of
electrostatic and electrodynamic physics using 4
simple field models
Electric Field of a Point Charge
For multiple charges:Fon q = F1on q + F2on q + F3on q + …
Enet = Fon q/q = F1onq/q + F2on q/q + F3on q/q + …
Enet = Ei (Principle of Superposition)
Simple Example of Superposition Principle
Limiting Cases & Typical Field Strengths
• Near an object, electric field depends on object shape and charge distribution
• Far away from the object, it appears to be a point charge• These are limiting cases. We will use limiting cases to help us
understand and simplify our discussion during class
Example of strongelectric field: ionizes the gasinside the field
The Electric Field of Multiple Point Charges
• Superposition Principle allows us to sum electric fields from all charges
• Often easier to break them into components and sum them for each unit vector, i,j,k
• See Problem Solving Strategy on p. 820 & example on p. 821
Determining Electric Field
Determining Electric Field
The Electric Field of a Dipole
• An electric dipole is two equal but opposite charges separated by a small distance s
The Electric Field of a Dipole
•An electric dipole is two equal but opposite charges separated by a small distance
•May be permanent or induced
•Has zero net charge
•Has an electric field
This is true for anypoint along the X-axis.
Dipole Moment
Units of dipole moment are Cm
The Electric Field of a Dipole
• An electric dipole is two equal but opposite charges separated by a small distance s
• Dipole moment p = qs
The Electric Field of a Dipole
• An electric dipole is two equal but opposite charges separated by a small distance s
• Dipole moment p = qs
• Field of a dipole drops off with distance much more quickly than a point charge(Why? It is electrically neutral.) Coulomb’s Law deals with point charges, not dipoles.
Are we violating Coulombs Law byHaving an r3 in theEquation?
Field Lines and Field Vectors
For a point charge, the field lines were straight in to the center or straight out from the center. For a dipole field lines are curved.
Another way to visualize an electricfield is to draw fieldlines instead of fieldvectors like we did inChapter 26.
Electric Field Lines• Continuous curves drawn tangent to field vectors,
therefore, field vector is tangent to field line• Spacing indicates field strength
– Closely spaced – strong field– Widely spaced – weak field
• Electric field lines never cross• Electric field lines start from positive charges and end
on negative charges• Draw arrows along field lines to indicate direction• Just because there is no field line drawn at a specific
point doesn’t mean that there is no field there. This is only a way to represent field
Using a Test Charge to Determine the Direction of the Force Due to the Dipole
Electric Field
Field lines follow the directionof the force measured (orequivalently – the electricfield vectors).
Force is parallelto field vectors
Visualizing the Electric Field of a Dipole
Using a Test Charge to Determine the Direction of the Force Due to
Multiple Charges
Electric Field of a Continuous Charge
• We will view a collection of atoms making up an extended 3-D object as continuous matter. This discussion will be based upon this view.
• Any charged metal object will, since it is a conductor, be uniformly charged over its entire surface – we will consider this to be continuous charge (we will assume it is uniformly charged unless specified otherwise)
• Use Q for the total charge on the metal object
Linear Charge Density
Linear chargedensity units areC/m
Surface Charge Density
Surface charge densityunits are C/m2
Finding Electric Field of a Line Charge
Finding Electric Field of a Line Charge
Check out Problem Solving Strategy on page 826
Electric Field of an Infinite Line of Charge
• Decreases more slowly than for a point charge (1/r)
• This will be approximately true for any r<<L– The field is defined by the closest charges to the
point of interest – Outlying points too far away to have much effect
• Realistic finite line charges can be approximated using the equation above
Electric Field For an Infinite Line of Charge
Electric Field For a Ring of Charge
Electric Field For a Ring of Charge
Electric Field For a Disk of Charge
Electric Field For a Plane of Charge
Electric Field For a Plane of Charge
Electric Field For a Sphere of Charge
The Parallel Plate Capacitor
The Parallel Plate Capacitor
Motion of a Charged Particle in an Electric Field
• Established forces on a charge in an electric field
• Net force means acceleration (motion)• F = ma = mv2/r = qE• a = qE/m = constant if field is uniform• Motion in a non-uniform field can be very
complicated• One simple example of motion in a non-
uniform field is orbital motion such as a negatively charged particle around a positive charge
Motion of a Charged Particle in an Electric Field
F = |q|E = mv2/r
Circular Motion of a Charge
Motion of a Dipole in an Electric Field
A Sample of Permanent Dipoles Align to the Electric Field
Motion of a Dipole in an Electric Field
Examples of Dipoles in aNon-Uniform
Field
Dipoles in a non-uniform electricfield will experience a net force.
Backup Slides