A small bead of mass m, carrying a charge q, is constrained to slide along a thin rod of length L. Charges Q are fixed at each end of the rod.(adsbygoogle = window.adsbygoogle || []).push({});

a) Obtain an expression for the electric field due to the charges Q as a function of x, where x is the distance from the midpoint of the rod. (Answer is kQ[(L/2+x)^-2 - (L/2-x)^-2]^I)

b) Show that for x << L, the magnitude of the field is proportional to x.

c) Show that if q is of the same sign as Q as, the force that acts on the object mass m is always directed toward the center of the rod and is proportional to x.

d) Find the period of the oscillation of the mass m if it is displaced by a small distance from the center of the rod and then released. (Answer is 2 * pi * sqrt(mL^3 /32kqQ) ).

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So part (a) was pretty easy. I just did E = kQ/r^2 – kQ/r^2 and got the book answer.

The next three parts i don't know what to do. For part (d) i know that T = 2 pi * sqrt(m / k).

Then i did kx = qE to solve for "k" of spring, plugged in E, but it left me with some overly complicated equation.

Anyways, thanks for any help in advance.

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# Homework Help: Electric Field/Oscillation Problem

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