First slide

Coulumbs law

Question

Two identical small charged spheres A and B , each carrying a charge Q are suspended from a point O by two light non-conducting strings each of length l = 1m. Equilibrium separation between the spheres is found to be 10 mm. Now some more charge is supplied to the spheres so that charge on each sphere becomes 8Q. Then new equilibrium separation between the spheres is

Difficult

A

60 mm
B

80 mm
C

20 mm
D

40 mm

Solution

(4)
$\begin{array}{l} T \sin θ = F = \frac{1}{4 π ε_{0}} \frac{Q^{2}}{x^{2}} \\ T \cos θ = m g \\ ∴ \tan θ = \frac{Q^{2}}{4 π ε_{0} m g . x^{2}} \\ Sin c e x < < l, \tan θ \approx \sin θ = \frac{x / 2}{l} \\ ∴ \frac{x}{2 l} = \frac{Q^{2}}{4 π ε_{0} m g x^{2}} . \\ \Rightarrow x = {(Q)}^{2 / 3} . {(\frac{l}{2 π ε_{0} m g})}^{1 / 3} \Rightarrow x \propto {(Q)}^{2 / 3} \\ ∴ \frac{x_{2}}{x_{1}} = {(\frac{Q_{2}}{Q_{1}})}^{2 / 3} \Rightarrow \frac{x_{2}}{10} = {(\frac{8 Q}{Q})}^{2 / 3} = 4 \\ \Rightarrow x_{2} = 40 m m \end{array}$

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