1. Dan Merrill Office: Room 164 Office Hours: W,F (12:00 – 1:00 pm)
Course Homepage
CHIP

2. Housekeeping Lectures slides on course website ~1 hour before class
CHIP
Homework assignments are answered in CHIP
Assignments are due on Fridays by 11:59 pm with two exceptions
Lectures
If I speak too quickly, let me know
If I speak too softly, let me know
If you don’t understand something, let me know

3. Review Charge: (C) Electric Force: (N) A property of matter
Two types: (+) and (-)
Electric Force: (N)
Requires at least two particles (or an external field)
Summarized in Coulomb’s Law

4. Review Electric Field: (N/C) Gauss’s Law:
Force per unit positive test charge
Needs only one charged particle
Represented by electric field lines
(-) charges spontaneously move against direction of field lines
Gauss’s Law:
Relates charge to electric flux, not electric field
Can be used to find electric field for simple geometries
Point, sphere, line, barrel, sheet

5. Conductors and Insulators
Conductors (metals)
Charge moves around
Excess charge is all on the surface
E field inside is zero
Entire object can be charged
Insulators
No conduction (movement) of charge
Extra charge stays where it is placed

6. Shielding the Electric Field
A region can be designed to have zero electric field
Go inside a metal cavity
Field in metal is zero
Field in cavity is zero
Gauss’s law
Examples:
Your car — shields you from a lightning strike
Most Basements— why you lose cell phone reception
Section 18.2 6

7. Example: E field? Long metal rod surrounded by metal sheath
+Q on rod
-Q on sheath
What is the electric field?
E0-R1 = ?
ER1-R2 = ?
ER2-R3 = ?
ER3-Infinity = ?

8. Polarization
Section 17.4

9. Polarization, cont.
There can be an electric force on an object even when the object is electrically neutral
The paper remains electrically neutral
The negative side of the paper is repelled
The positive side of the paper is closer to the rod so it will experience a greater electric force
Coulomb’s Law
Polarization can happen with both conductors and insulators
Induction in metals
Section 17.4

10. Balloons
Section 17.4

11. Charging by Induction Induction makes use of polarization
The charged rod is first brought near the metal, polarizing the metal
A connection is made from the piece of metal to electrical ground
Electrical ground is a large sea of charge that can act as a source or sink
Usually is physically the ground (i.e. earth)
The electrons are able to use the wire to move even farther from the charged rod
Removing the wire leaves the metal with a net positive charge
Section 17.4

12. Review Charge and Coulomb’s Law: Electric Field:
Electric Flux and Gauss’s Law:
Gauss’s law applies to closed surfaces
Conductors and Insulators
Polarization, Induction, and Ground

13. Chapter 18
Electric Potential

14. Electric Potential Energy
From mechanics,
Work, W = F Δx
Change in Potential Energy, ΔPE = - W
We can find the change in electric potential energy,
F = q E
ΔPEelec = -q E Δ x
ΔPEelec gives the change in potential energy of the charge as it moves through displacement Δ x in a direction parallel to E.
Section 18.1

15. Electric Potential Energy, cont.
Electric field is a conservative field,
ΔPEelec is path independent
ΔPEelec only depends on the net parallel displacement ∆x ∆x
Section 18.1

16. Two Point Charges
From Coulomb’s Law, we know there is a force between the two particles
Movement under a force requires a change in energy
If they are like charges, they will repel
Potential energy increases from ri to rf
If they are unlike charges, they will attract
Potential energy decreases from ri to rf
Section 18.1

17. Two Point Charges, cont.
PEelec approaches a constant value when the two charges are very far apart
r becomes infinitely large
The electric force also approaches zero in this limit
By convention, we set zero potential energy at infinity (usually)
Other places could be set as “zero potential energy”
Section 18.1

18. Two Point Charges, cont. The electric potential energy is given by
Gives the energy required to move q1 from infinity to r in the presence of q2, or vice versa
Note that it is the change in energy that matters
There is no absolute potential energy
Value depends on zero reference
Section 18.1

19. PEelec and Superposition
The results for two point charges can be extended by using the superposition principle
If there is a collection of point charges, the total potential energy is the sum of the potential energies of each pair of charges
Complicated charge distributions can always be treated as a collection of point charges arranged in some particular matter
The electric forces between a collection of charges will always be conservative
Section 18.1

20. Example: Total Potential Energy?

21. Electric Potential
The electric potential is defined as the change in potential energy required to move a positive test charge from infinity to a particular point in space per unit test charge
Often referred as “the potential”
As E is to F, so too V is to PEelec
Units are the Volt, V
1 V = 1 J/C
Section 18.2

22. Electric Potential, cont.
The electric potential at a distance r away from a single point charge q is given by
Since changes in potential (and potential energy) are important, a “reference point” must be defined
The standard convention is to choose V = 0 at r = ∞
In many problems, the Earth may be taken as V = 0
This is the origin of the term electric ground
Section 18.2

23. Electric Potential and Field
The magnitude and direction of the electric field are related to how the electric potential changes with position
There can be a point with zero electric field and a non-zero potential, and vice versa
Section 18.2

24. Electric Field Near a Metal
The field outside any spherical ball of charge is given by
The field is still zero inside a metal
Section 18.2

25. Potential Near a Metal
Since the field outside the sphere is the same as that of a point charge, the potential is also the same
The potential is constant inside the metal
Section 18.2

26. Equipotential Surfaces
A useful way to visualize electric fields is through plots of equipotential surfaces
Contours where the electric potential is constant
Equipotential surfaces are in two-dimensions
Are always perpendicular to electric field
Section 18.3

27. Equipotential Surface – Point Charge
The electric field lines emanate radially outward from the charge
The equipotentials are a series of concentric spheres
Different spheres correspond to different values of V
Section 18.3

28. Summary Vector Scalar 2-particle Force: (N) Potential Energy: (J)
1-particle
Electric Field: (N/C)
Potential: (V)

29. Capacitors
A capacitor uses potential difference to store charge and energy
Applying a potential difference between the plates induces opposite charges on the plates
Example:
parallel-plate capacitor
clouds
Section 18.4

30. Capacitance Defined
Capacitance is the amount of charge that can be stored per unit potential difference
The capacitance is dependent on the geometry of the capacitor
For a parallel-plate capacitor with plate area A and separation distance d, the capacitance is
Unit is farad, F
1 F = 1 C/V
Section 18.4

31. Energy in a Capacitor, cont.
Storing charge on a capacitor requires energy
Requires energy to move a charge ΔQ through a potential difference ΔV
The energy corresponds to the shaded area in the graph
The total energy stored is equal to the energy required to move all the packets of charge from one plate to the other
Section 18.4

32. Energy in a Capacitor, cont.
The total energy corresponds to the area under the ΔV – Q graph
Energy = Area = PEcap
Q is the final charge
ΔV is the final potential difference
Section 18.4

33. Energy in a Capacitor, Final
From the definition of capacitance, the energy can be expressed in different forms
These expressions are valid for all capacitors
Section 18.4

34. Dielectrics
Most real capacitors contain two metal “plates” separated by a thin insulating region
Many times these plates are rolled into cylinders
The region between the plates typically contains a material called a dielectric
Section 18.5

35. Dielectrics, cont.
Inserting the dielectric material between the plates changes the value of the capacitance
The change is proportional to the dielectric constant, κ
Cvac is the capacitance without the dielectric and Cd is with the dielectric
κ is a dimensionless factor
Generally, κ > 1, so inserting a dielectric increases the capacitance
Section 18.5

36. Dielectrics, final
When the plates of a capacitor are charged, the electric field established extends into the dielectric material
Most good dielectrics are highly ionic and lead to a slight change in the charge in the dielectric
Since the field decreases, the potential difference decreases and the capacitance increases
Section 18.5

37. Uses of Capacitance