A small metallic sphere carrying a charge 2 10⁻⁶ C is suspended using a thin thread of negligible mass from a rigid support, in a horizontal electric filed 5 10^4 Vm ⁻¹ . If the thread is making an angle 30^0 with the vertical, What is the tension in the thread?

Step-by-step solution

Let q = 2 10⁻⁶ C be the charge on the sphere, E = 5 10^4 Vm ⁻¹ be the electric field, and = 30^ be the angle the thread makes with the vertical. The forces acting on the sphere are the gravitational force mg acting downwards, the electric force F_e = qE acting horizontally, and the tension T in the thread. In equilibrium, the forces are balanced: T = qE T = mg From the first equation, T = qE . Substituting the given values: T = (2 10⁻⁶ C ) (5 10^4 Vm ⁻¹) 30^ T = 10⁻¹ 1 2 T = 0.1 2 = 0.2 N Answer: 0.2 N