Two identical conducting silver cubes (initially uncharged) are attached to the

Question

Two identical conducting silver cubes (initially uncharged) are attached to the ends of a horizontal massless spring. Each cube has a mass of 50 grams and are considered to be point particles. The cubes are initially at rest on a frictionless surface. The spring constant of the spring is

k = 125 N/m

. The equilibrium length of the spring is

x0 = 37.0 cm.

Each cube is given identical amounts of a positive charge +q. The repulsive electric force between the cubes stretches the spring by 15.0 cm. Find the charge q on each cube?

Explanation / Answer

The hook's force will be:

F(hooks) = kx = 125 x 0.15 = 18.75 N

This force should be equal to the electrostatic force.

F(electrostatic) = F(hooks)

kq^2/r^2 = 18.75

q = sqrt (18.75 x r^2/k)

q = sqrt (18.75 x 0.37^2/9 x 10^9) = 1.69 x 10^-5 C

Hence, charge on each cube = q = 1.69 x 10^-5 C = 17 uC

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