(a) From the expression for obtained in Example 22.9 (Section 22.4), find the expression for the electric potential V as a function of r both inside and outside the uniformly charged sphere. Assume that V = 0 at infinity. (b) Graph V and E as functions of from r = 0 to r = 3R.

Solution 72P Step 1 of 2: a)The potential difference between two points a and b, also called the potential of a with respect b to b, is given by the line integral of V aV = E.dl b a The field radially outward , so E.dl = Edr Let a = , so V = a r If r > R, E = k2 and V = kQ d2= kQ r r r R r If r < R, E = 3Q and V = E.dr= ( kQ k3 )r d r R R R R kQ kQ kQ = R + 2R R3 2 = kQ (3 r2) 2R R