Example: A positively charged (+ q ) metal sphere of radius r a is inside

1. Our first exam is next Tuesday - Sep 27. It will cover everything I have covered in class including material covered today. There will be two review sessions Monday, Sep 26 - at 12:30 PM and at 3:00 PM in the same room as the problem solving session: FN 2.212. 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: 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

3. 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

4. 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

5. 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

6. 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)

7. 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

8. 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) CapacitanceC (1 Farad = 1 Coulomb / 1 Volt) is determined by pure geometry (and insulator properties) 1 Farad IS very BIG: Earth’s C < 1 mF

9. 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

10. 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

11. Capacitance configurations Cylindrical capacitor Spherical Capacitance

12. Definitions • Equivalent Capacitor—a single capacitor that has the same capacitance as a combination of capacitors. • Parallel Circuit—a circuit in which a potential difference applied across a combination of circuit elements results in the potential difference being applied across each element. • Series Circuit—a circuit in which a potential difference applied across a combination of circuit elements is the sum of the resulting potential differences across each element.

13. Capacitors in Series

14. Capacitors in Parallel Example: Voltage before and after