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)
$$\begin{gathered} \Rightarrow \tan \theta =\frac{qE}{mg} \\ =\frac{20\times {10}^3\times 2\times {10}^{-8}}{80\times {10}^{-6}\times 9.8} \end{gathered}$$
$$\begin{gathered} \Rightarrow \tan \theta =\frac{5}{9.8} \\ \Rightarrow \theta =27° \end{gathered}$$
From equation (1),
$$\begin{gathered} T=\frac{mg}{\mathrm{cos\theta }}=\frac{80\times {10}^{-6}\times 9.8}{\cos 27°} \\ \Rightarrow T=8.8\times {10}^{-4}\mathrm{N} \end{gathered}$$