Question

A small 2g plastic ball is suspended by a 20 cm long string in a uniform electric field. If the ball is in equilibrium when the string makes a 15 degree angle with the vertical, what is the net charge on the ball? E=10^3 N/c(answer: 5.25x10^-6)

Work:
I know E=q/r^2
10^3=q/(.2m)(cos15)

Answer 1

The answer depends upon the direction of the applied electric field. Is it horizontal?

Let's assume that it is, and that the string tenston force is T. In that case
T cos 15 = M g
T sin 15 = Q E
tan 15 = Q E/(M g) = 0.268
g is the acceleration of gravity and M is the mass.
Solve for Q . Make sure M is in kg

The length of the string does not matter, but the angle does.

Answer 2

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Answer 3

What if the electric field is not horizontal?