A small sphere with mass 1.50g hangs by a thread between two parallel vertical plates 5cm apart. THe plates are insulating ahnd have uniform surface charge densities + and - [tex]\sigma[/tex]. The charge on the shpere is q = 8.90 x 10^-6 C. What potential difference between the plates will cause the the thread to assume an angle of 30 degrees with the vertical?
Va->b = Ex
E = [tex]\sigma[/tex]/[tex]\epsilon[/tex]0
Va->b = [tex]\sigma[/tex]d/[tex]\epsilon[/tex]0
The Attempt at a Solution
I am actually a little stuck as to where to begin, I know the sphere orginally hangs on its string at x = .025m, and since the opposing plates are oppositely charged the positive sphere is attracted to the negative plate and raised a certain distance at an angle of 30 degrees.
would I be right in assuming I could find the magnitude of the surface charge density utilizing the potential with formula kq/r, with r = .025m; then use that density in the equation with potential at r = .025cos30 (the point where the shpere is pulled by the negative plate)?
so it would turn out like this:
[tex]\sigma[/tex] = [tex]\epsilon[/tex]0V.025->0/.05
then use this value in the equation:
Va->b = [tex]\sigma[/tex].025cos30/V.025->0
any help is greatly appreciated.