Lecture07_Kim

Lecture07_Kim - Lecture 7-1 Calculation of V for Continuous...

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1 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: ( 29 P V r E dl ∞→ = - a ca a (2) Integrate dV (contribution to V(r) from each infinitesimal source charge dq ) over all source charges: h A line integral (which could be tricky to do) h 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 dV r = = = 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 dV 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 Lecture 7-4 Reference Point for Potential of Uniformly Charged Sheet For x > 0, 0 0 0 , ( ) (0) 2 ( ) 2 , (0) Integrating V x x V V x k x V V V σ ε π σ = - + = - + = A similar derivation for x < 0 can be combined to obtain for both x > 0 and x < 0 : 0 ( ) 2 | | V x k x V = - + P x O equipotential 0 2 dV E dl dx = - • = - a a
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2 Lecture 7-5 Potential from uniformly charged spherical shell Potential r > R : r < R : ( ) r l Q V r E dl k r =∞ = - = a a Electric field (Gauss’s Law) r < R: E = 0 r > R: E = kQ/r 2 ( ) r R r r r l R Q V r E dl E dr E dr k R =∞ = - = - - = a a 0 (or a charged solid spherical conductor ) + + + + + + 0, r E E r R = = Lecture 7-6 Electric Field of a Uniformly
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This note was uploaded on 02/05/2012 for the course PHYS 241 taught by Professor Wei during the Spring '08 term at Purdue.

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Lecture07_Kim - Lecture 7-1 Calculation of V for Continuous...

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