1. My office change was not reflected on the syllabus. It is now ESCN 2
Our first exam is a week from next Tuesday - Sep 27. It will cover everything I have covered in class including material covered next Thursday.
There will be two review sessions Monday, Sep at 12:30 PM and at 3:00 PM in the same room as the problem solving session: FN
I have put several (37) review questions/problems on Mastering Physics. These are not for credit but for practice. I will review them at the review session Monday.

2. Example: Potential between oppositely charged parallel plates
From our previous examples
Easy way to calculate surface charge density
Remember! Zero potential doesn’t mean the conducting object has no charge! We can assign zero potential to any place, only difference in potential makes physical sense

3. Example: Charged wire We already know E-field around the wire
only has a radial component
Vb = 0 – not a good choice as it follows
Why so?
We would want to set Vb = 0 at
some distance r0 from the wire
r - some distance from the wire

4. Example: Sphere, uniformly charged inside through volume
Q - total charge
- volume density of charge
This is given that at infinity j =0

5. Potential Gradient We can calculate potential difference directly
Components of E in terms of j
Frequently, potentials (scalars!) are easier to calculate:
So people would calculate potential and then the field
Superposition for potentials: V = V1 + V2 + …

6. Example: A positively charged (+q) metal sphere of radius ra is inside
of another metal sphere (-q) of radius rb. Find potential at different points
inside and outside of the sphere. -q 1 a) 2 +q
Total V=V1+V2 b) c)
Electric field between spheres

7. Equipotential Surfaces
Equipotential surface—A surface consisting of a continuous distribution of points having the same electric potential
Equipotential surfaces and the E field lines are always perpendicular to each other
No work is done moving charges along an equipotential surface
For a uniform E field the equipotential surfaces are planes
For a point charge the equipotential surfaces are spheres

8. Equipotential Surfaces
Potentials at different points are visualized by equipotential surfaces (just like E-field lines).
Just like topographic lines (lines of equal elevations).
E-field lines and equipotential surfaces are mutually perpendicular

9. Definitions cont Electric circuit—a path through which charge can flow
Battery—device maintaining a potential difference V between its terminals by means of an internal electrochemical reaction.
Terminals—points at which charge can enter or leave a battery

10. Definitions
Voltage—potential difference between two points in space (or a circuit)
Capacitor—device to store energy as potential energy in an E field
Capacitance—the charge on the plates of a capacitor divided by the potential difference of the plates C = q/V
Farad—unit of capacitance, 1F = 1 C/V. This is a very large unit of capacitance, in practice we use F (10-6) or pF (10-12)

11. Capacitors
A capacitor consists of two conductors called plates which get equal but opposite charges on them
The capacitance of a capacitor C = q/V is a constant of proportionality between q and V and is totally independent of q and V
The capacitance just depends on the geometry of the capacitor, not q and V
To charge a capacitor, it is placed in an electric circuit with a source of potential difference or a battery

12. CAPACITANCE AND CAPACITORS
Capacitor: two conductors separated by insulator and charged by opposite and equal charges (one of the conductors can be at infinity)
Used to store charge and electrostatic energy
Superposition / Linearity: Fields, potentials and potential differences, or voltages (V), are proportional to charge magnitudes (Q)
(all taken positive, V-voltage between plates)
Capacitance C (1 Farad = 1 Coulomb / 1 Volt) is determined by pure geometry (and insulator properties)
1 Farad IS very BIG: Earth’s C < 1 mF

13. Calculating Capacitance
Put a charge q on the plates
Find E by Gauss’s law, use a surface such that
Find V by (use a line such that V = Es)
Find C by

14. Parallel plate capacitor
Energy stored in a capacitor is related to the E-field between the plates
Electric energy can be regarded as stored in the field itself.
This further suggests that E-field is the separate entity that may exist alongside charges.
Generally, we find the potential difference
Vab between conductors for a certain
charge Q
Point charge potential difference ~ Q
This is generally true for all capacitances

15. Cylindrical capacitor
Capacitance configurations
Cylindrical capacitor
Spherical Capacitance