Sphere-Shell_Potential

0 we can find the electric potential at the origin by

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Unformatted text preview: A. If it were otherwise, it would imply an electric field within the solid sphere and that is not possible for a conductor in static equilibrium. 0! ˆ We can find the electric potential at the origin by calculating: !V = " % E # r dr . We $ can break this out into the region r > rC, rA < r < rB. %1 1( rC kQ rA kQ kQ 2 1 !V = V (0 ) = " $ dr " $ dr = 2 + kQ1 ' " * # rB r2 r2 rC & rA rB ) We can think of this situation in terms of superposition of electric potentials, but we must be carful! There are three charged spherical surfaces with respective charges, Q1,  ­Q1, and Q2. The potential on any of the 3 surfaces is that of a point charge at the origin. Once inside a given surface, the potential due to that surface charge does not change. Therefore, we can simply write down the solution: Potential at the origin due to charge Q2 is VQ2 (0 ) = so V (0 ) = VQ1 (0 ) + V!Q1 (0 ) + VQ2 (0 ) = "1 1% kQ2 + kQ1 $ ! ' rC # rA rB & kQ2 kQ kQ , V!Q1 (0 ) = ! 1 , VQ1 (0 ) = 1 , rC rB rA...
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