Question

Two small spheres, each with a mass of 20 g, are suspended from a common point by two insulating strings of length 40 cm each. The spheres are identically charged and the separation between the balls at equilibrium is found to be 4 cm. Find the charge on each sphere. 

Answer 1

 

Tcosθ = mg   ...(i)
Tsinθ = F_e   ...(ii)
Here,  

\[F_e  = \frac{1}{4 \pi\epsilon_0}\frac{q^2}{r^2}\]

\[\tan\theta = \frac{2}{39 . 9}\]

Dividing equation (ii) by (i), we get

\[\tan\theta = \frac{F_e}{\text{ mg }}\] 

\[ \Rightarrow \tan\theta = \frac{1}{4 \pi\epsilon_0}\frac{q^2}{r^2} . \frac{1}{\text{mg}}\] 

\[ \Rightarrow  q^2  = \frac{\tan\theta . r^2 . \text{mg}}{1/4 \pi\epsilon_0}\] 

\[ \Rightarrow  q^2  = 17 \times  {10}^{- 16} \] 

\[ \Rightarrow q = 4 . 123 \times  {10}^{- 8}   C\]