Question

A pendulum bob of mass 80 mg and carrying a charge of 2 × 10⁻⁸ C is at rest in a uniform, horizontal electric field of 20 kVm⁻¹. Find the tension in the thread.

Answer 1

Given:
Magnitude of the charge, q =  2.0 × 10⁻⁸ C
Mass of the bob, m = 80 mg = 80 × 10⁻⁶ kg
Electric field, E = 20 kVm⁻¹ = 20 × 10³ Vm⁻¹
Let the direction of the electric field be from the left to right. Tension in the string is T.
From the figure, 

Tcosθ = mg    ...(1) 
Tsinθ = qE    ...(2)

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

$$=\frac{20\times {10}^3\times 2\times {10}^{-8}}{80\times {10}^{-6}\times 9.8}$$

$$\Rightarrow \tan \theta =\frac{5}{9.8}$$ 

$$\Rightarrow \theta ={27}^{\circ }$$

From equation (1),

$$T=\frac{mg}{cos\theta }=\frac{80\times {10}^{-6}\times 9.8}{\cos {27}^{\circ }}$$ 

$$\Rightarrow T=8.8\times {10}^{-4}$$N