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Electric Potential (II)

Electric Potential (II). Potential of a point charge Potential of several point charges Potential energy of a collection of charges. Review: Electric Potential. Electric potential is not an absolute quantity. It is always relative to the potential V=0 for our choice of position.

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Electric Potential (II)

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  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! ). riare distances! q1 A At A: q2 In General: • (for a discrete charge distribution) • (for a continuous charge distribution) Or…

  7. a Quiz: a a A single charge q produces a potential V0 = 1000 V at point O. a +q O a) What is the potential at point O due to the two identical charges? +q a a a • 1000 V • 1414 V • 2000 V • 2828 V a +q O 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 O b L Total charge Q, uniform linear charge density Find: V at point O (So =Q/L )

  9. Solution

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

  11. Solution

  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) q2 r12 q1 Potential due to q1 at q2 is Potential energy of pair of charges is: This is the work we do, W=∆U.

  13. q2 r12 q1 r23 r13 q3 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)

  14. a Quiz: a a A single charge q=1mC produces a potential V0 = 1000 V at point O. a +q O +q +q a Find the total potential energy of the four identical charges? a a a +q +q

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

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