1. Un importable:
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Practice Exam 1 has been posted on course web site
1 hand graded question and 5 multiple choose questions

2. Question 1 (Chap. 16)
A solid metal ball carrying negative excess charge is placed near a uniformly charged plastic ball. -Q +Q
metal
plastic
Which one of the following statements is true?
The electric field inside both balls is zero.
The electric field inside the metal ball is zero, but it is nonzero inside the plastic ball.
The electric fields inside both objects are nonzero and are pointing toward each other.
The electric field inside the plastic ball is zero, but it is nonzero inside the metal ball.
Answer: B

3. Question 2 (Chap. 16) Which one of these statements is false?
The electric field of a very long uniformly charged rod has a 1/r distance dependence.
The electric field of a capacitor at a location outside the capacitor is very small compared to the field inside the capacitor.
The fringe field of a capacitor at a location far away from the capacitor looks like an electric field of a point charge.
The electric field of a uniformly charged thin ring at the center of the ring is zero.
Answer: C It looks like a dipole field!

4. Integration
Divide shell into rings of charge, each delimited by the angle  and the angle +
Use polar coordinates (r, ,).
Distance from center: d=(r-Rcos)
Surface area of ring:
R  R
Rsin 
Rcos d r

5. A Solid Sphere of Uniformly Distributed Charge
What if charges are distributed throughout an object?
Step 1: Cut up the charge into shells R
For each spherical
shell:
outside: r E
inside: dE = 0
Outside a solid sphere of charge:
for r>R

6. A Solid Sphere of Uniformly Distributed Charge
Inside a solid sphere of charge: R E r
for r<R
Why is E~r? 
On surface:

7. Chapter 17
Electric Potential

10. Exercise
What is the electrical potential at a location 1Å from a proton? 1Å
What is the potential energy of an electron at a location
1Å from a proton?
Or in atomic units eV.

11. Exercise 2Å 1Å
What is the change in potential in going from 1Å to 2Å from the proton?
What is the change in electric potential energy associated with moving an electron from 1Å to 2Å from the proton?
Does the sign make sense?

12. Potential Energy
To understand the dynamics of moving objects consider:
forces, momenta, work, energy
Introduced the concept of electric field E to deal with forces
Introduce electric potential – to consider work and energy
Electric potential: electric potential energy per unit charge
Practical importance:
Reason about energy without having to worry about the details of some particular distribution of charges
Batteries: provide fixed potential difference
Predict possible pattern of E field

13. Electric Potential Energy of Two Particles
Potential energy is associated with pairs of interacting objects
Energy of the system:
Energy of particle q1
Energy of particle q2
Interaction energy Uel q2
r12 q1
Esystem = E1+E2+Uel
To change the energy of particles we have to perform work.
E1 is a single particle energies = rest energy plus KE.
Wext – work done by forces exerted by other objects
Wint – work done by electric forces between q1 and q2
Q – thermal transfer of energy into the system

14. Electric Potential Energy of Two Particlesq2
r12
Uel  -Wint q1 if
Total energy of the system can be changed (only) by external forces.
Scalar product of 2 vectors! F here is the force between two charged particles, ie, the Coulomb force.
Work done by internal forces:

15. Electric Potential Energy of Two Particlesq2 q2 q1 q1
Uel > 0 for two like-sign charges
(repulsion)
Uel < 0 for two unlike-sign
Charges (attraction)

16. Electric and Gravitational Potential Energyq1 q2 m1 m2

17. Three Electric Charges
Interaction between q1 and q2 is independent of q3
There are three interacting pairs:
q1  q2
q2  q3
q3  q1
U12
U23
U31
U= U12+ U23+ U31

18. Multiple Electric Chargesq1 q3 q6
Each (i,j) pair interacts:
potential energy Uij q2 q5 q4

19. Electric Potential
Electric potential  electric potential energy per unit charge
Alessandro Volta ( )
Units: J/C = V (Volt)
Volts per meter = Newtons per Coulomb
Electric potential – often called potential
Electric potential difference – often called voltage

20. V due to One Particle Single charge has no electric potential energyq2
Single charge has potential to interact with other charge –
it creates electric potential
probe charge
J/C, or Volts

21. V due to Two Particles Electric potential is scalar:
Electric potential energy of the system: q3
If we add one more charge at position C:

22. V at Infinity
r, V=0
Positive charge
Negative charge

23. Question 1
What is the potential in the center of uniformly charged hollow sphere? ([k=1/(4pe0)])
k*Q/R2
k*Q/R
k*Q/(4pR2)
Not enough information Q R B

24. Potential Inside a Uniformly Charged Hollow Sphere=0