Consider a uniformly charged sphere of radius R and total

Chapter 26, Problem 26.114

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Consider a uniformly charged sphere of radius R and total charge Q. The electric field Eout outside the sphere 1r R2 is simply that of a point charge Q. In Chapter 24, we used Gausss law to find that the electric field Ein inside the sphere 1r R2 is radially outward with field strength Ein = 1 4pP0 Q R3 r a. The electric potential Vout outside the sphere is that of a point charge Q. Find an expression for the electric potential Vin at position r inside the sphere. As a reference, let Vin = Vout at the surface of the sphere. b. What is the ratio Vcenter /Vsurface? c. Graph V versus r for 0 r 3R

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