A simple pendulum has a bob with mass m and charge q . The pendulum string has negligible mass. When a uniform and horizontal electric field E is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is _ _ _ _ . (g: acceleration due to gravity)

Step-by-step solution

The charged bob experiences two forces at equilibrium: Gravitational force: F_g = mg (downward) Electric force: F_E = qE (horizontal, in direction of field) These forces are perpendicular to each other. The string tension must balance their resultant. At equilibrium, the string makes angle with vertical such that: Vertical: T = mg Horizontal: T = qE The net force from gravity and electric field is (mg)^2 + (qE)^2 Therefore, the tension in the string is: T = m^2g^2 + q^2E^2