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Question
A simple pendulum consists of a small sphere of mass m suspended by a thread of length l. The sphere carries a positive charge q. The pendulum is placed in a uniform electric field of strength E directed vertically downwards. Find the period of oscillation of the pendulum due to the electrostatic force acting on the sphere, neglecting the effect of the gravitational force.
Solution
The length of the thread = l
Mass of the sphere = m
Charge on the sphere = +q
Force on sphere due to a downward electric field = qE (downward)
As the gravitational force is neglected hence net force on the conductor is the force due to the electric field. i.e.
Fnet = qE
So-net acceleration = `"qE"/"m"`
Hence the time period of the pendulum is `"T" = 2pi sqrt("l"/(("qE"/"m"))) = 2pi sqrt("ml"/"qE")`
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