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I have the following. A stationary ring of radius a lies in the yz plane and has a uniform positive charge Q. A small particle that has mass m and a negative charge -q is located at the center of the ring. (a) show that is x << a the electric field along the axis of the ring is porportional to x. (b) find the force on teh particle as a function of x. (c) show that if the particle is given a small displacement in the +x direction, it will perform SHM.

So for (a), do I do, since the E for a ring is k*Q*x/(a^2+x^2)^(3/2), where x is the displacement on the z axis, and a is the radius. So that's a because if x is very small then the equation is basically k*Q*x/a^3. So this is porportional to x.

(b) Then wouldn't the force just be q*E, and since there's a negative charge -q here, wouldn't the F = q*k*Q*x/a^3?

(c) So to show SHM, I need to show that acceleration = some constant w^2*displacement. So couldn't I just set q*k*Q/a^3 as w?

Thanks!!