Lecture 6-1 Please read the textbook before each Lecture and Come to the lecture with questions The chapter to be covered is at the end of the syllabus

Lecture 6-2 Thin sheet of any charge distribution Just to left of disk Just to right of disk tiny disk

Lecture 6-3 Electrostatic Shielding (Continued) 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’’ If you move charge q in the cavity, the exterior electric fields and the extreior charge distribution are not affected. Conducting shell electrostatically shields its exterior from changes on the inside. q Conducting shell electrostatically shields its interior from changes on the outside, too.

Lecture 6-4 Gravitational vs Electrostatic Potential Energy a b GravityCoulomb b a

Lecture 6-5 Electric Potential Energy of a Charge (continued) i is “the” reference point. Choice of reference point (or point of zero potential energy) is arbitrary. 0 i is often chosen to be infinitely far ( )

Lecture 6-6 Potential Energy in the Field due to a Point Charge q From ∞ This is also called the potential energy of the two-charge configuration of q and q 0.

Lecture 6-7 Potential Energy of a Multiple-Charge Configuration

Lecture 6-8 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. An electron would have a higher potential energy at point A than at point B B. A proton would have a higher potential energy at point A than at point B C. An electron would have a lower potential energy at point A than at point B D. The potential energy is the same for an electron and a proton at point A. E.The potential energy is the same for a proton at point A and point B. A B -q

Lecture 6-9 Electric Potential So U(r)/q 0 is independent of q 0, allowing us to introduce electric potential V independent of q 0. U(r) of a test charge q 0 in electric field generated by other source charges is proportional to q 0. taking the same reference point

Lecture 6-10 Potential at P due to a point charge q From ∞ V(r) drop following the direction of electrical field.

Lecture 6-11 Electron Volt V=U/q is measured in volts => 1 V (volt) = 1 J / 1 C V depends on an arbitrary choice of the reference point. V is independent of a test charge with which to measure it. (electron volt) Potential energy difference when 1 C of charge is moved between points of potential difference 1 V

Lecture 6-12 Potential due to two (source) charges

Lecture 6-13 Potential due to Multiple Source Charges: Example Dotted line is an equipotential when q 1 =12nC, q 2 = - 24nC, q 3 =31nC, q 4 =17nC

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

Lecture 6-15 Lightning E = 3 x 10 6 N/C at electrical breakdown of air V on the order of 10 9 V

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

Lecture 6-17 Physics 241 –Quiz 4a A spherical shell is uniformly charged with a positive charge density . Which of the following statements is (are) true? Select one of (a) – (e). 1. An electron would have a higher potential energy at point A than at point B 2. A proton would have a higher potential energy at point A than at point B 3. The electric potential is lower at A than at B 4. The electric potential is higher at A than at B A B a)1 and 3 only b)1 and 4 only c)2 and 3 only d)2 and 4 only e)None of them 

Lecture 6-18 Physics 241 –Quiz 4b A plane is uniformly charged with a positive charge density . Which of the following statements is (are) true? Select one of (a) – (e). 1. A proton would have a higher potential energy at point A than at point B 2. An electron would have a higher potential energy at point A than at point B 3. The electric potential is lower at A than at B 4. The electric potential is higher at A than at B A B a)1 and 3 only b)1 and 4 only c)2 and 3 only d)2 and 4 only e)None of them 

Lecture 6-19 Physics 241 –Quiz 4c A sphere is uniformly charged with a negative surface charge density . Which of the following statements is (are) true? Select one of (a) – (e). 1. A proton would have a higher potential energy at point A than at point B 2. An electron would have a higher potential energy at point A than at point B 3. The electric potential is lower at A than at B 4. The electric potential is higher at A than at B A B a)1 and 3 only b)1 and 4 only c)2 and 3 only d)2 and 4 only e)None of them 