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Lecture07_Kim

Lecture07_Kim - Calculation of V for Continuous Charge...

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Lecture 7-1 Calculation of V for Continuous Charge Distributions Two Ways to Calculate Potential (1) Integrate - E from the reference point ( ) to the point ( P ) of observation:   P V r E dl    (2) Integrate dV (contribution to V(r) from each infinitesimal source charge dq ) over all source charges: A line integral (which could be tricky to do) If E is known and simple and a simple path can be used, it may be reduced to a simple, ordinary 1D integral. q 1 q 2 q 3 q 4 P Q P r P Q / i i kdq V kq r V r

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Lecture 7-2 Potential from continuous charge distribution: ring At point P on axis of ring Sum scalar contributions dV 2 2 kdq k kQ V dq r r r kQ V x a
Lecture 7-3 Potential and Field of a Ring At point P on axis of ring 2 2 kQ V x a vector x V(x) 2 2 3/2 ( ) 0 x y z V x E kQ x x a E E   x E x

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Lecture 7-4 Reference Point for Potential of Uniformly Charged Sheet For x > 0, 0 0 0 0 ( ) (0) 2 ( ) 2 , (0) x V x E dl x V V x k
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Lecture07_Kim - Calculation of V for Continuous Charge...

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