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# lecture9 - El ectr i c Potenti a l(I I I Fi el ds Potenti...

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Electric Potential (I I I) - Fields - Potential - Conductors

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Potential and Continuous Charge Potential and Continuous Charge Distributions Distributions We can use two completely different methods: 1. 1. Or, Find from Gauss’s Law, then… , r dq k dV e = = source e r dq k V E , s d E dV - = - = - B A A B s d E V V
Potential and Electric Field Potential and Electric Field Since y V E y V E x V E y y x - = - = - = , s d E dV - = therefore, we have: Hence: V k z V j y V i x V E - = + + - = ) (

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Ex 1: Given V=3x 2 y+y 2 +yz, find E.
Ex 2: Find the potential of a finite line charge at P, AND the y-component of the electric field at P. dq r L x d P

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Solution
Example: The Electric Potential of a Example: The Electric Potential of a Dipole Dipole Find : a) Potential V at point P. b) What if x>>a ? c) Find E. x y P +q -q a a

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Solution
Example: Find the potential of a uniformly charged sphere of radius R, inside and out. R

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Uniformly Charged Sphere,radius R R r E R r V
Recall that the electric field inside a solid conducting sphere with charge Q on its surface is zero. Outside the sphere the field is the same as the field of a point charge Q

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