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),

\[T = \frac{mg}{cos\theta} = \frac{80 \times {10}^{- 6} \times 9 . 8}{\cos27^\circ}\] 

\[ \Rightarrow T = 8 . 8 \times  {10}^{- 4} \]N