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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.

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#### 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.

F_{net }= 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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