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3. A Little Bundle of Jey Charge: The electric field of a solid bal of charge, Q, with radius R is given by: T E (a) Calculate the divergence of E g spherical coordinates and components) at a point inside and a point outside the sphere to show that you obtain the correct result from Gausss law V.E-) (b) Assume a reference point of roo e., V(oo)). Detere the electric potential at all (c) Now assume a reference point of ro-0(i.c., V(0-0). Determine the electric potential at all (d) On separate plots, graph the magnitude of the electric field and the electric potential as functions points as a function of r points as a function of r for this case. Compare your result with part (b) of r froin 0 to somewhere outside the sphere (nssume ro = oo). Are the plots of E(r) and V(r) continuous? Are their slopes continus? Justify any discontinuities. (e) How would your answers to parts (b) and (d) change if, instead of a solid sphere, we had a spherical shell with radius R and total (surface) charge Q?
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