A small nonconducting charged ball of mass m = 0.0033kg and charge q = 4.3 mu C

Question

A small nonconducting charged ball of mass m = 0.0033kg and charge q = 4.3 mu C hangs by an insulating thread connected to an infinitely large vertical nonconducting sheet of uniformly distributed charge. The ball is suspended in static equilibrium. The angle that the thread subtends with the sheet is 27 degree a) What is the surface charge density of the sheet ? b) What if the ball broke off of the thread? What would be the magnitude and direction of the ball's acceleration the instant that the ball broke away from the thread? c) What if instead of a sheet, the thread was connected to an infinitely large conducting surface? What would be the surface charge density of the surface for the equilibrium condition of the ball?

Explanation / Answer

A) here tan theta = Eq/mg

tan 27 degree = sigma q/ (2eo*mg)

sigma = tan 27 degree (2eo*mg)/q

= tan 27 degree * 2*8.85e-12 *0.0033*9.8/4.3e-6

= 6.783*10^-8 C/m^2

B) T cos 27 degree = mg and T=ma

a = g/ cos 27 degree

= 9.8/ cos 27 degree

= 11 m/s^2

B) Then the surface charge density would not be uniform and will be very difficult to calculate. The charges on the surface will get influenced by the charge of the ball.

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