A pendulum bob having a mass of 80 mg and carrying a charge of 2 10⁻⁸ C remains at rest in a uniform horizontal electric field of 20 kV m ⁻¹ . Determine the tension in the thread.

Step-by-step solution

Given, mass of the bob, m = 80 mg = 80 10⁻⁶ kg Charge on the bob, q = 2 10⁻⁸ C Electric field, E = 20 kV m ⁻¹ = 2 10⁴ V m ⁻¹ The electric force acting on the bob horizontally is: F_ e = qE = (2 10⁻⁸ C )(2 10⁴ V m ⁻¹) = 4 10⁻⁴ N The gravitational force acting on the bob vertically downwards is: W = mg = (80 10⁻⁶ kg )(9.8 m s ⁻²) = 7.84 10⁻⁴ N Since the bob is at rest, the tension T in the thread balances the resultant of the electric force and the weight. Since F_ e and W are perpendicular to each other, the tension