quiz 2 solution - b q b q dr dr q r d r E r V r b b r r 1 4...

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A hollow, uncharged spherical conductor has inner radius a and outer radius b. A positive point charge +q is in the cavity at the center of the sphere. Assume that V=0 at r = . a) Find the potential V(r) for r b b) Find the potential V(r) for a r b c) Find the potential V(r) for r a d) Sketch the electric potential V(r) as a function of r. First find the electric field in all three regions: For r b: For a r b: For r a: r q r E 2 4 ) ( ε ο π = 0 = E r q r E 2 4 ) ( = Now for parts a, b, and c we can use the equation r d r E R V R r r = ) ( ) ( For r b: r q r q dr q r d r E r V r r r 1 4 1 1 4 4 ) ( ) ( 2 = = = = r r For a r b:
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Unformatted text preview: b q b q dr dr q r d r E r V r b b r r 1 4 1 1 4 4 ) ( ) ( 2 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∞ − = − − = • − = ∫ ∫ ∫ ∞ ∞ r r +q a b For a ≥ r ≥ b: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∞ − = = − − − = • − = ∫ ∫ ∫ ∫ ∞ ∞ r a b q a r q b q dr q dr dr q r d r E r V r a a b b r r r 1 1 1 4 1 1 4 1 1 4 4 4 ) ( ) ( 2 2 ε ο π r r Graph: Potential (V) Radius a b...
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This document was uploaded on 02/05/2011.

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quiz 2 solution - b q b q dr dr q r d r E r V r b b r r 1 4...

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