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The electric field of a uniformly charged ring centered at the origin and laying on the...

The electric field of a uniformly charged ring centered at the origin and laying on the xy plane is given by

E = (Q/4πε0)[ z/(z 2 + a 2)3/2] ˆk,

where a is the radius of the ring and Q is its total charge.

Show that a small test charge −q (q > 0) with mass m will undergo simple harmonic motion with an angular frequency

ω = [qQ/4πε0ma3 ]1/2

for |z|<< a.

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