Chapter 26, Problem 81EAP

Consider a uniformly charged sphere of radius R and total

charge Q. The electric field $E_{OUT}$ outside the sphere $(r\ge R)$ ) is

simply that of a point charge Q. In Chapter 24, we used Gauss's

law to find that the electric field E_in inside the sphere $(r\le R)$ is radially outward with field strength.

$E_{in}=\frac{1}{4\pi \epsilon }\frac{Q}{R^3}r$

1. The electric potential V_out 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 V_in = V_out the surface of the sphere.

What is the ratio $V_{CETNTRE}/V_{SURFACE}$ ?

Graph V versus r for $0\le r\le 3R$ .