Chapter 21 Electric Potential

1. Chapter 21 Electric Potential

2. + + + + charged Conservative force Conservation of energy Potential (energy) air → conductor Potential difference (voltage) discharge 2

3. Coulomb force is conservative Comparing : Electrostatic / Coulomb force is conservative Work doesn’t depend on the path: The circulation theorem of electric field 3

4. - + Electric potential Conservative force → potential energy U U depends on the charge! Define electric potential: Potential difference / voltage: 4

5. a b Electric potential & electric field Difference in potential energy between a and b: If position b is the zero point: Relationship between electric field and potential Unit of electric potential: Volt (V) 5

6. . a Q Zero point Electric potential: It depends on the chosen of zero point Usually let V = 0 at infinity: For the field created by a point charge : 6

7. Properties of electric potential 1) Va→potential energy per unit (+) charge 2) Va depends on the zero point, Vba does not 3) Va and Vba are scalars, differ from E vector 7

8. . A r Calculation of electric potential If the electric field is known: Potential of point charge: (V = 0 at infinity) System of several point charges: 8

9. . h l l . . Potential of electric dipole Example1: (a) Determine the potential at o, a, b. (b) To move charge q from a to b, how much work must be done? Solution: (a) (b) 9

10. a + . + + + + + + + + + Q Charged conductor sphere Example2: Determine the potential at a distance r from the center of a uniformly charged conductor sphere (Q, R) for (a) r>R; (b) r=R; (c) r < R. Solution: All charges on surface: (a) V at r>R: Same as point charge 10

11. c b . . + + + + + + + + + + + + + Q ? - - - (b) V at r=R: (c) V at r<R: Same potential at any point! Discussion: (1)Conductor: equipotential body (2)Charges on holey conductor 11

12. b . x dx dQ a d L Uniformly charged rod Example3: A thin rod is uniformly charged (λ, L). Determine the potential for points along the line outside of the rod. Solution: Choose infinitesimal charge dQ Potential at point b? 12

13. .a r x Q dQ R Charged ring Example4: A thin ring is uniformlycharged (Q, R).Determine the potential on the axis. Solution: or: Discussion: (1)Not uniform? (2)x >> R (3)other shapes 13

14. a h R Conical surface Question: Charges are uniformly distributed on a conical surface (σ, h, R).Determine the electric potential at top point a. (V = 0 at infinity) 14

15. - Q + - + - + - + R - q + - + o b Electrostatic induction Question:Put a charge q nearby a conductor sphere initially carrying no charge. Determine the electric potential on the sphere. Connect to the ground? 15

16. Q R *Breakdown voltage Air can become ionized due to high electric field Air → conducting → charge flows Breakdown of air: Breakdown voltage for a spherical conductor? 16

17. Equipotential surfaces Visualize electric potential: equipotential surfaces Points on surface → same potential (1) Surfaces ⊥ field at any point. (2) Move on surface, no work done (3) Move along any field line, V ↘ (4) Surfaces dense → strong field 17

18. Some examples (1) Equipotential surfaces for dipole system: (2) Conductors (3) Parallel but not uniform field lines? 18

19. Component of E in the direction of dl : E determined from V To determine electric field from the potential, use In differential form: Total electric field: 19

20. V+dV V dn  a b dl 1 2 Gradient of V Gradient of V : Gradient → partial derivative in direction V changes most rapidly 20

21. Determine E from V Example5: The electric potential in a region of space varies as V = x2yz. Determine E. Solution: 21

22. Example6: The electric field in space varies as . Determine V. Determine V from E Solution: ( C is constant ) 22