A conducting sphere in electrostatic equilibrium has charge Q and radius R. (a) Find the electric potential at a distance r > R from the center of the sphere, assuming that the potential at large distances from the sphere is 0 V. Hint: find the electric field, and then perform an integral. (b) Find the electric potential at a distance r < R from the center of the sphere, assuming that the potential at large distances from the sphere is 0 V. Hint: remember that the sphere is in equilibrium. (c) Use your results from (a) and (b) to graph the electric potential as a function of r. Clearly indicate the sphere radius R on the horizontal axis.
A
(a) Find the electric potential at a distance r > R from the center of the sphere, assuming that the potential at large distances from the sphere is 0 V.
Hint: find the electric field, and then perform an integral.
(b) Find the electric potential at a distance r < R from the center of the sphere, assuming that the potential at large distances from the sphere is 0 V.
Hint: remember that the sphere is in equilibrium.
(c) Use your results from (a) and (b) to graph the electric potential as a function of r. Clearly indicate the sphere radius R on the horizontal axis.
(d) In the above, we assumed that the potential very far away from the sphere was 0 V. This is just a conventional reference value, though, and only potential differences matter. How would your answers to (a) and (b) change if we assumed that the potential very far away from the sphere was 10 V? That is, write expressions for the potential at distances r < R and r > R with this new reference point.
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