Question

In the figure, two conducting balls of identical mass m = 25 g and identical charge q hang from nonconducting threads of length L = 100 cm. If x = 6.7 cm, what is q? Since x is much smaller than L approximate sin(?) by ?.

Answer 1

In the x direction, the sum of forces are the x component of the tension and the electrical force.

The equation in the x direction is Tsin(angle) = kq^2/r^2

In the y direction, the sum of forces are the y component of the tension and the weight.

The equation in the y direction is Tcos(angle) = mg

Divide x equation by y equation and get

tan(angle) = kq^2/mgr^2

The angle is found from the sin function

sin(angle) = 3.35/100

angle = 1.92 degrees

tan(1.92) = (9 X 10^9)(q^2)/(.025)(9.8)(.067)^2

q = 6.40X 10^-8 C (that is 64.0 nC)