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.

 

 

Answers (1)

Let's determine the period of oscillation of the pendulum due to the electrostatic force acting on the sphere.

let, f=-q\; E\; \sin \phi (Restoring force)

       ma=-q\; E\; \sin \phi

When, \phi is small

Then, ma=-q\; E\; \phi

m\frac{d^{2}x}{dt^{2}}=-qE\; \frac{x}{l}

\frac{d^{2}x}{dt^{2}}=-q\; \frac{E}{m}\; \frac{x}{l}

On comparing with the equation of linear SHM.

\frac{d^{2}x}{dt^{2}}=-w^{2}x

w=\sqrt{\frac{qE}{ml}}

\therefore T=\frac{2\pi }{w}=2\pi \sqrt{\frac{ml}{qE}}

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