A bob of a simple pendulum has a mass of 4 g and a charge of 20 C . If it is at rest in a uniform horizontal electric field of intensity 1000 Vm ⁻¹ , the angle that the pendulum makes with the vertical at equilibrium is:

Step-by-step solution

The forces acting on the bob at equilibrium are the gravitational force mg acting vertically downwards, the electric force qE acting horizontally, and the tension T in the string. Let be the angle the string makes with the vertical. At equilibrium, the forces balance as follows: T = qE T = mg Dividing the two equations, we get: = qE mg Given values are m = 4 g = 4 10⁻³ kg , q = 20 C = 20 10⁻⁶ C , E = 1000 Vm ⁻¹ , and taking g = 10 ms ⁻² : = (20 10⁻⁶) 1000 4 10⁻³ 10 = 20 10⁻³ 40 10⁻³ = 20 40 = 1 2 Therefore, = ⁻¹ (