Electric Potential II

• Conductors (in electrostatic equilibrium)
• Electric Field is zero in conductor.



• Any excess charge is all on surface.



• Electric field is perpendicular to surface



• Charge will accumulate at sharp points



• Potential of a Charged Conductor
• The surface of a charged conductor is an equipotential surface.





• The potential inside the conductor is constant and equal to the value of the surface.





• Finding the field from the potential
• we used E to determine V, but if we have determined V by some other means, we can use that to find the electric field
• because V is a scalar, it is sometimes easier to find than E.
• We know that a small change in the electric potential is given by



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• suppose that the electric field only has an x-component. Then:



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• or
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• The electric potential may depend on y and z, in addition to x. Same idea holds for y and z. However, if the potential depends on x, y, and z, then we must use partial derivatives instead of ordinary derivatives.



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• When you take the partial derivative of V with respect to x, you treat y and z as constant and similarly for derivatives with respect to y and z.



• Example

• Continuous Charge Distributions
• What is the potential at point P
• reference point ( V = 0 @ r = infinity)
• break distribution into small pieces and sum up the potential
• contribution from each piece



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• total potential



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• if the pieces are too big, make them smaller, limiting conditions



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• Examples