Electrostatics Part 3

Concept:In equilibrium, the net force on the bob is zero.The tension in the string balances both the weight and the electric force.Explanation:Let the string make an angle $\theta$ with the vertical.Resolve the tension into components:Vertical component: $T \cos \theta$ balances weight $mg$ → $T \cos \theta = mg$.Horizontal component: $T \sin \theta$ balances electric force $qE$ → $T \sin \theta = qE$.Square and add: $T^2(\sin^2 \theta + \cos^2 \theta) = (mg)^2 + (qE)^2$.Since $\sin^2 \theta + \cos^2 \theta = 1$, we get $T^2 = m^2 g^2 + q^2 E^2$.Therefore, $T = \sqrt{m^2 g^2 + q^2 E^2}$.Answer:Option B: $\sqrt{m^2 g^2 + q^2 E^2}$