Quiz8-2007-102

Quiz8-2007-102 - center of the sphere. Outsite the sphere,...

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a) What is the surface charge density on the surface of the sphere. 2 4 R Q Area Q π σ = = b) Find and plot the magnitude of the electric field E inside and outside the sphere. The sphere is a conductor therefore electric field inside is zero: 0 = inside E , r < R Outside the sphere, there is an electric field due to the charge enclosed by the surface: 2 2 4 4 r Q E Q r E A d E Q A d E πε ε = = = = r r r r r For r > R, E decreases as r goes to infinity. c) Find and plot the potential V , inside and outside the sphere. = = r d E V V V i f r r Let , a reference potential at the initial point. Then for E=0, r < R, we have 0 V V i = () () () 0 0 0 0 V r V r d V r V V r V V f = = = = = r This holds for r < R as well as for r = R. Up to now we see that there is a constant potential inside the sphere, and this potential is same as the reference potential at the
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Unformatted text preview: center of the sphere. Outsite the sphere, r > R, we have calculated that 2 4 r Q E πε = r and we know that ∫ ∫ − = ⋅ − = − = ∆ r R i f dr r Q r d E V V V 2 4 r r ( ) ( ) ( ) ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⋅ + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − ⋅ − = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ⋅ − = − = − = ∆ ∫ R r Q R V r V R r Q r Q dr r Q R V r V V r R r R 1 1 4 1 1 4 1 4 1 4 2 Right when r = R, we have ( ) ( ) R V r V = ; for r > R potential starts to decrease, approaching zero as r goes to infinity....
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This note was uploaded on 04/23/2010 for the course -- -- taught by Professor -- during the Spring '10 term at Bilkent University.

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Quiz8-2007-102 - center of the sphere. Outsite the sphere,...

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