1. Lecture 7-1 Gravitational vs Electrostatic Potential Energy a b GravityCoulomb b a

2. Lecture 7-2 E from V Potential are the same everywhere on a conductor

3. Lecture 7-3 Electric Potential Energy and Electric Potential negative charge High U Low U positive charge High U (potential energy) Low U High V (potential) Low V Electric field direction High V Low V Electric field direction

4. Lecture 7-4 Reference Point for Potential of Uniformly Charged Infinite Sheet Take a reference point at O. Or take it at some other point so that V(0)=V 0 : P x O equipotential since V=V(x)

5. Lecture 7-5 Potential from uniformly charged spherical shell Potential r > R: r < R: Electric field (Gauss’s Law) r < R: E = 0 r > R: E = kQ/r 2 0 (or a charged solid spherical conductor) + + + + + +

6. Lecture 7-6 Potential of a Uniformly Charged (solid) Sphere (2) r < R (1) r > R (  same as shell or conducting sphere) (very different!) V r R + + + + + + + insulator

7. Lecture 7-7 Physics 241 –warm-up quiz A infinite plane with uniform charge density +σ. What is the potential difference V B -V A ? AB 1 m 2 m +σ.+σ. a)  (3/2)  /  0 b)  /2  0 c)3  /  0 d)  /2  0 e)  3  /  0

8. Lecture 7-8 Charged Concentric Spherical Conductors (a) r > c a b c Q in Q out r V (b) b < r < c (c) a < r < b (d) r < a

9. Lecture 7-9 Potential from continuous charge distribution: ring At point P on axis of ring Sum scalar contributions dV vector

10. Lecture 7-10 Potential and Field of a Ring At point P on axis of ring vector x V(x) x ExEx

11. Lecture 7-11 High Electric Field at Sharp Tips Two conducting spheres are connected by a long conducting wire. The total charge on them is Q = Q 1 +Q 2. Potential is the same: The smaller the radius of curvature, the larger the electric field. With same potential, sphere with smaller radius carry smaller amount of charge

12. Lecture 7-12 Lightning rod Air “Break down” before too much charge accumulated, i.e. much weaker lightning which is much less destructive. Golf court

13. Lecture 7-13 Equipotential Surfaces An equipotential surface is a surface on which the potential is the same everywhere. Equipotential surfaces are drawn at constant intervals of  V Potential difference between nearby equipotentials is approximately equal to E times the separation distance. E  an equipotential surface everywhere. Equipotential surfaces

14. Lecture 7-14 Potential of a Uniformly Charged Sheet Electric field is uniform on each side of the sheet as shown. Equipotential surfaces are  to the electric fields. Separation between equipotential surfaces are equal to the potential differences divided by the magnitude of electric field.

15. Lecture 7-15 Physics 241 –Quiz 5a A spherical shell of radius 50 cm is charged uniformly with a total charge of +Q Coulombs. What is the potential difference V B -V A ? a)kQ/2 b)-2kQ c)-(3/2)kQ d)kQ e)-kQ/2 Q AB 1 m 2 m

16. Lecture 7-16 Physics 241 –Quiz 5b Two parallel planes, 2 m apart, are charged with uniform charge densities 2  and  (in C/m 2 ). Respectively as shown. What is the potential difference V B -V A (in volts)? a)  (3/2)  /  0 b)  2  /  0 c)3  /  0 d)  /  0 e)  3  /  0 AB 2 m

17. Lecture 7-17 Physics 241 –Quiz 5c A spherical shell of radius 20 cm is charged uniformly with a total charge of Q Coulombs. What is the potential difference V B -V A ? a)kQ/2 b)-2kQ c)-(3/2)kQ d)kQ e)-kQ/2 Q AB 1 m 2 m