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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.
Solution
Tcosθ = mg ...(i)
Tsinθ = Fe ...(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
\[\tan\theta = \frac{F_e}{\text{ mg }}\]
\[ \Rightarrow \tan\theta = \frac{1}{4 \pi\epsilon_0}\frac{q^2}{r^2} . \frac{1}{\text{mg}}\]
\[ \Rightarrow q^2 = \frac{\tan\theta . r^2 . \text{mg}}{1/4 \pi\epsilon_0}\]
\[ \Rightarrow q^2 = 17 \times {10}^{- 16} \]
\[ \Rightarrow q = 4 . 123 \times {10}^{- 8} C\]
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