Electric force:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{{\mathbf{kq}}_{\mathbf{1}}{\mathbf{q}}_{\mathbf{2}}}{{\mathbf{r}}^{\mathbf{2}}}}$

Newton's second law:

$\overline{){\mathbf{F}}{\mathbf{=}}{\mathit{m}}{\mathit{a}}}$

q = -q_{0}

E = kqz/(z^{2} + a^{2})^{(3/2)}

F = -kqq_{0}z/(z^{2} + a^{2})^{(3/2)}

at a point z = d,

F = -kqq_{0}d/(d^{2} + a^{2})^{(3/2)}

When d << a, (d^{2} + a^{2}) is approximately equal to a^{2}

F = -kqq_{0}d/a^{3} = (-kqq_{0}/a^{3})d

Consider a uniformly charged ring in the *xy* plane, centered at the origin. The ring has radius **a** and positive charge **q** distributed evenly along its circumference.

Imagine a small metal ball of mass **m** and negative charge -q_{0}. The ball is released from rest at the point **(0, 0, d)** and constrained to move along the *z-axis*, with no damping. If 0 < d << a, what will be the ball's subsequent trajectory?

A. repelled from the origin

B. attracted toward the origin and coming to rest

C.oscillatingalong the *z-axis* between z = d and z = -d.

D. circling around the *z-axis* at z =d

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