Question 14

The bob of a simple pendulum has mass 2 g and a charge of 5.0 $$\mu$$C. It is at rest in a uniform horizontal electric field of intensity 2000 V/m. At equilibrium, the angle that the pendulum makes with the vertical is: (take g = 10 m/s$$^{2}$$)

At equilibrium, the forces acting on the bob are:

Weight (mg) vertically downward

Electric force (qE) horizontally

Therefore,

$$\tan\theta=\frac{qE}{mg}$$

Substituting the values,

$$\tan\theta= \frac{5\times10^{-6}\times2000} {2\times10^{-3}\times10}$$

$$\tan\theta= \frac{10\times10^{-3}} {20\times10^{-3}}$$

$$\tan\theta=\frac{1}{2}$$

Hence,

$$\theta=\tan^{-1}(0.5)$$

$$\boxed{\theta \approx 26.6^\circ}$$

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