A tiny ball of mass m and charge q is suspended from the fixed support using an insulating string of length 1 ~m . The horizontal uniform electric field E is switched on. The angle made by the string with vertical when the ball is in equilibrium is 45^ . The magnitude of uniform electric field is

Step-by-step solution

Let the mass of the ball be m , charge be q , and the electric field be E . The forces acting on the ball in equilibrium are: 1. Gravitational force mg acting vertically downwards. 2. Electric force qE acting horizontally. 3. Tension T in the string acting along the string at an angle = 45^ with the vertical. Resolving the forces into horizontal and vertical components: Horizontal direction: T = qE Vertical direction: T = mg Dividing the two equations: T T = qE mg = qE mg Given = 45^ , we have 45^ = 1 . 1 = qE mg E