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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 it 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)
Forces on bob in equilibrium:
Weight downward
mg
Electric force horizontal
qE
Tension T along string balancing resultant of these two.
Since equilibrium requires tension equal to resultant of perpendicular forces:
$$T=\sqrt{(mg)^2+(qE)^2}$$
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