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)
S safeer

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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