- #1
barnsworth
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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.
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.
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.