1. Electric Potential (II) Potential of a point charge Potential of several point charges Potential energy of a collection of charges

2. Review: Electric Potential Electric potential is not an absolute quantity. It is always relative to the potential V=0 for our choice of position. Most often we choose V=0 at the position of infinity.

3. What is the electric potential at distance r from a point charge Q? +Q r

4. Solution

5. Eg: a) What shape are the equipotential surfaces near an isolated point charge? b) What is the potential 10 cm from an isolated point charge of 100 nC ? c) What is the potential 10 cm from an isolated point charge of -100 nC ?

6. Potential of Several Point Charges Potentials add (as scalars! ). r i are distances! A q1q1 q2q2 At A: In General: Or…  (for a continuous charge distribution)  (for a discrete charge distribution)

7. Quiz Quiz: +q a a a a O A single charge q produces a potential V 0 = 1000 V at point O. +q a a a a O a) What is the potential at point O due to the two identical charges? A)1000 V B)1414 V C)2000 V D)2828 V b) How much work is done by the field to move a 1 nC test charge from O to the centre of the square?

8. Example: Thin Uniformly Charged Rod L + + + + + + + + + + + + + + + + + O b Total charge Q, uniform linear charge density (So =Q/L ) Find: V at point O

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10. Example: Uniformly Charged Disk Total charge Q, uniform charge density σ Find: V at the point P P a

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12. Electrostatic Potential Energy What is the total potential energy of 2 point charges? How much work would we have to do to assemble the charges from infinity? (Note: we assume U = 0 when all point charges are at infinity) q2q2 q1q1 r 12 Potential due to q 1 at q 2 is Potential energy of pair of charges is: This is the work we do, W=∆U.

13. What is the total potential energy of 3 (or more) point charges? How much work would we have to do to assemble the charges from infinity? (again, assume U = 0 when all point charges are at infinity) q2q2 q3q3 q1q1 r 23 r 13 r 12

14. Quiz Quiz: +q a a a a O A single charge q=1  C produces a potential V 0 = 1000 V at point O. +q a a a a Find the total potential energy of the four identical charges? +q

15. Summary Potential of a point source: (scalar, “absolute” potential) Several point charges: Potential energy: 2 Point Charges, 3 Point Charges,