Chapter 13, Problem 13.35E

(a)

To determine

The gravitational potential energy $U$ of the system.

(b)

To determine

The expression for the gravitational potential energy $U$ of the system reduces to the expected result when $x$ is much larger than the radius $a$ of the ring.

(c)

To determine

The magnitude and the direction of the force on the particle.

(d)

To determine

The expression for the force on the particle reduces to the expected result when $x$ is much larger than the radius $a$ of the ring

(e)

To determine

The values of $U$ and $F_{\text{x}}$ when $x=0$.