Thin sheet of any charge distribution tiny disk Just to right of disk Just to left of disk

Charges and fields of a conductor In electrostatic equilibrium, charges inside a conductor do not move. Thus, E = 0 everywhere in the interior of a conductor. Since E = 0 inside, there are no net charges anywhere in the interior. Net charges can only be on the surface(s). The electric field must be perpendicular to the surface just outside a conductor, since, otherwise, there would be currents flowing along the surface.

Electrostatic Shielding (Continued) If you move charge q in the cavity, the exterior electric fields and the extreior charge distribution are not affected. q Conducting shell electrostatically shields its exterior from changes on the inside. Add Q’ If you now add charge Q’ to the conductor and/or Q’’ on the outside of the conductor, the interior electric fields do not change. Q’’ + Conducting shell electrostatically shields its interior from changes on the outside, too.

READING QUIZ 1 IN WHAT DIRECTION CAN YOU MOVE A TEST CHARGE RELATIVE TO AN ELECTRIC FIELD SO THAT THE ELECTRIC POTENTIAL DOES NOT CHANGE? A| Move in the direction of the electric field lines. B| Move opposite to the direction of the electric field lines. C| Move from point A in the electric field to point B in in the electric field along an arbitrary path. D| Move relative to the electric field along a path which is everywhere perpendicular to the electric field.

Electric Potential Energy of a Charge in Electric Field Coulomb force is conservative => Work done by the Coulomb force is path independent. Can associate potential energy to charge q0 at any point r in space. It’s energy! A scalar measured in J (Joules)

Electric Potential Energy of a Charge (continued) i is “the” reference point. Choice of reference point (or point of zero potential energy) is arbitrary. i is often chosen to be infinitely far away (∞)

Gravitational vs Electrostatic Potential Energy b Gravity Coulomb (if g, E uniform) Work done by gravity or the Coulomb force decreases the potential energy.

Potential Energy in the Field due to a Point Charge q From ∞ The potential drops along a field line! This is also called the potential energy of the two-charge configuration of q and q0. What is the work required to bring q0 in from infinity?

Potential Energy of a Multiple-Charge Configuration (b) (c)

Physics 241 –Warm-up quiz Three point charges carry the same charge -q. Which of the following statements is true? Select one of (a) – (e). A B -q An electron would have a higher potential energy at point A than at point B A proton would have a higher potential energy at point A than at point B An electron would have a lower potential energy at point A than at point B The potential energy is the same for an electron and a proton at point A. The potential energy is the same for a proton at point A and point B.

Scalar! Electric Potential U(r) of a test charge q0 in electric field generated by other source charges is proportional to q0 . So U(r)/q0 is independent of q0, allowing us to introduce electric potential V independent of q0. taking the same reference point [Electric potential] = [energy]/[charge] SI units: J/C = V (volts) A positively charged particle produces a positive electric potential; a negatively charged particle produces a negative electric potential. Scalar! Potential energy difference when 1 C of charge is moved between points of potential difference 1 V

Potential at P due to a point charge q From ∞ The potential drops along a field line!

POTENTIAL DIFFERENCES V2 – V1 Electron Volt V=U/q is measured in volts => 1 V (volt) = 1 J / 1 C POTENTIAL DIFFERENCES V2 – V1 (electron volt) V depends on an arbitrary choice of the reference point. V is independent of a test charge with which to measure it.

Potential due to two (source) charges

Potential due to Multiple Source Charges: Example Dotted line is an equipotential when q1=12nC, q2= -24nC, q3=31nC, q4=17nC

Lecture 6-16 E from V We can obtain the electric field E from the potential V by inverting the integral that computes V from E: Expressed as a vector, E is the negative gradient of V

Lightning E = 3 x 106 N/C at electrical breakdown of air ΔV on the order of 109 V http://micro.magnet.fsu.edu/electromag/java/lightning/index.html

DOCCAM 2 5A-16 PROOF PLANE

Examples (only a Preview) Point charge Q: Uniformly charged sphere: r > R r < R Charged disk: Charged sheet: Charged line:

Physics 241 – 10:30 Quiz 3 September 8, 2011 A spherical shell is uniformly charged with a positive charge density σ. Which of the following statements is (are) true? Select one of (a) – (e). An electron would have a higher potential energy at point A than at point B A proton would have a higher potential energy at point A than at point B The electric potential is lower at A than at B The electric potential is higher at A than at B 1 and 3 only 1 and 4 only 2 and 3 only 2 and 4 only None of them σ A B

Physics 241 – 11:30 Quiz 3 September 8, 2011 A sphere is uniformly charged with a negative charge density. Which of the following statements is (are) true? Select one of (a) – (e). A proton would have a higher potential energy at point A than at point B An electron would have a higher potential energy at point A than at point B The electric potential is lower at A than at B The electric potential is higher at A than at B 1 and 3 only 1 and 4 only 2 and 3 only 2 and 4 only None of them -σ A B

Physics 241 – 10:30 Quiz 3 January 27, 2011 A sphere is uniformly charged with a negative charge density. Which of the following statements is (are) true? Select one of (a) – (e). A proton would have a higher potential energy at point A than at point B An electron would have a higher potential energy at point A than at point B The electric potential is lower at A than at B The electric potential is higher at A than at B 1 and 3 only 1 and 4 only 2 and 3 only 2 and 4 only None of them +3σ A B

Physics 241 – 11:30 Quiz 3 January 27, 2011 A sphere is uniformly charged with a positive surface charge density. Which of the following statements is (are) true? Select one of (a) – (e). A proton would have a higher potential energy at point A than at point B An electron would have a higher potential energy at point A than at point B The electric potential is lower at A than at B The electric potential is higher at A than at B 1 and 3 only 1 and 4 only 2 and 3 only 2 and 4 only None of them +3σ A B