A narrow, negatively charged ring of radius R exerts a force on a pos- itively charged particle P located at distance x above the center of the ring of magnitude kx F(x) = = = (x2 + R2)3/2 where * > 0 is a constant (Figure 10). (a) Compute the third-degree Maclaurin polynomial for F. (b) Show that F -(k/ R'jux to second order. This shows that when x is small, F(x) behaves like a restoring force similar to the force exerted by a spring. (c) Show that F(x) -k/x' when x is large by showing that F(x) lim x-+co -k/x] 1 Thus, F(x) behaves like an inverse square law, and the charged ring looks like a point charge from far away. F(x) Nearly linear here Nearly inverse square here FIGURE 10