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Lecture 10

# Lecture 10 - Electric Field and Potential Definitions...

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Definitions: q F E ! ! = q U V el = Electric Field and Potential Potential Difference: ! " = " = # f i l d F W U ! ! int ! " = # f i l d E V ! ! i f dl F ! " = " f i i f l d E V V ! ! In general, integration path may be complex Electric field is the negative gradient of potential: x V E x ! ! " = y V E y ! ! " = z V E z ! ! " = ! E = ! grad V = ! ! " V For very short path: l E V ! ! ! " = ! ! V = " E x ! x + E y ! y + E z ! z ( )

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What is E inside metal? E = 0 ! V = V f " V i = " ! E d ! l i f # What is the potential difference ( V f – V i ) ? 0 = ! V Is V zero everywhere inside a metal? No! But it is constant In static equilibrium Potential Difference in Metal In static equilibrium the electric field is zero at all locations along any path through a metal. ! V = " E x ! x + E y ! y + E z ! z ( ) The potential difference is zero between any two locations inside the metal, and the potential at any location must be the same as the potential at any other location. i f
Metal is not in static equilibrium: When it is in the process of being polarized When there is an external source of mobile charges (battery) ! V = " ! E d ! l i f # If a metal is not in static equilibrium, the potential isn’t constant in the metal. Potential in Metal Not in static equilibrium Nonzero electric field of uniform magnitude E throughout the interior of a wire of length L .

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Lecture 10 - Electric Field and Potential Definitions...

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