Chapter 22, Problem 66E

(a)

To determine

$\alpha$ in terms of $Q$ and $R$.

(b)

To determine

The expression for the magnitude of electric field for all the three regions and to check whether the answers agree on the boundaries of the regions.

(c)

To determine

The fraction of charge contained within the region $r\le \raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$.

(d)

To determine

To show: The motion of the electron is simple harmonic.

(e)

To determine

The period of motion in part (d).

(f)

To determine

Whether the motion in part (d) will be simple harmonic if the amplitude is greater than $\frac{R}{2}$.