Question

Two identical balls balls P and Q, each of mass 0.20 g, carry identical charges and are suspended by two threads of equal length. The balls position themselves at equilibrium such that the angle between the threads is 60_{o}.If the distance between the the balls is 0.5m, find the charge on each of them. Take g = 9.8 m/s^{2}

Answer 1

The charge on each of them is 0.173μC

Given the angle between the two  threads is 60° and the length of the two threads are equal.So, it forms an isoceles triangle so the other two angles will also be equal to 60°. Now,

Now, take a ball and we see that three forces act on it:

(i) Tension = T

(ii) Weight = mg

(iii) Electric force =  F (this will be replusive force because charges are same)

Tension T can be written as :

For equilibrium conditons, F = Tcos60°, mg = Tsin60°

Dividing, we get, $\frac{F}{mg} = cot 60$°

And we know, electric force , F = $k\frac {q^{2}}{r^{2}}$

thus, q = $\sqrt{ \frac{cot 60 . 9.8 . 0.20 * 10^{-3} * 0.25 }{9 * 10^{9} }$ 

          =  1.73 ×$10^{-7}$

         =  0.173μC