(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A negatively charged particle -q is placed at the center of a uniformly charged ring of radius a having positive charge Q. The particle, confined to move along the x-axis, is moved a small distance x along the axis (x << a) and released. Show that th eparticle oscillates in simple harmonic motion with a frequency given by

f = (1/2pi)(kqQ/ma^3)^(1/2).

2. Relevant equations

F = kq1q2/r^2

torque = r x F

torque = (I)(alpha)

I (moment of inertia) = mL^2 (L = distance from point about which rotation occurs, in this case, approx. L = a)

alpha = d^2(theta)/dt^2

*Where theta is angle between a and the hypotenuse in the triangle with base and height a and x.

3. The attempt at a solution

I tried finding net force on -q as exerted by the ring (relevant force is only in x direction)

F = -kQq/a(a-x) + kQq/a(a+x)

F = -2kQqx/a^3

then I plugged this into torque = r x F

where r is approx. a

and equated with torque = I(alpha)

which gave me the motion for simple harmonic motion d^2(theta)/dt^2 + 2kQqx(theta)/ma^4

(I made use of the limit lim(âˆ†theta-->0) sin(theta)/theta = 1)

and from this, the angular frequency should be (2kQqx/ma^4)^(1/2)

which gives f = (1/2(pi))(kQqx/ma^4)^(1/2)

which obviously isn't the answer.

What am I doing wrong?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Simple Harmonic Motion of Charges

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