physics question

Question

A small sphere with mass 2.10  hangs by a thread between two large parallel vertical plates  apart  The plates are insulating and have uniform surface charge densities  and . The charge on the sphere is  = 8.30×10⁻⁶ .

What potential difference between the plates will cause the thread to assume an angle of  with the vertical?

Answer 1

A couple comments before I start. In physics, units are critical. You have not given the mass units (I assume grams). You have not given charge unit (I assume coulombs). You have not given the angle at all. I will call it θ and assume it is an angle to the vertical...

Doing vertical and horizontal force balances:

1) F_W = mg = T_y = Tcos(θ)

2) F_E = qE = T_x = Tsin(θ)

If you take the ratio of equation 2 over equation 1 (eliminates T), you get,

qE/mg = tan(θ)

You can now solve for E. Note that m needs to be in kg.

Good luck and take care.