A small sphere with mass `1.2 g` hangs by a thread between two parallel vertical plates `5.00 cm` apart. The plates are insulating and have uniform surface charge densities `+ sigma and - sigma`. The charge on the sphere is `q = 9 xx 10^-6 C`. What potential difference between the plates will cause the thread to assume an angle of `37^(@)` with the vertical as shown in (Fig. 3.134) ?
.

Options

A. 30 V
B. 12 V
C. 50 V
D. 25 V

Answer

c

Explanation

`F_e = m g tan theta`
=`(1.20 xx 10^-3 kg)(10 ms^-2) tan (37^(@)) = 0.0090 N`
`F_e = E q = (V q)/D`
`:. V = (F_e d)/q = ((0.009 N)(0.0500 m))/(9.0 xx 10^-6 C) = 50.0 V`.