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Electric Circuit and Circuit Diagram

A particle of...

Question

A particle of mass m and charge q is attached to a light rod of length L. The rod can rotate freely in the plane of paper about the other end, which is hinged at P. The entire assembly lies in a uniform electric field E also acting in the plane of paper as shown. The rod is released from rest when it makes an angle $θ$ with the electric field direction. (Assume gravity free space)

Direction of angular acceleration changes alternatively

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θ

is small, the particle performs SHM

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The speed of the particle when the rod is parallel to the electric field is

{(\frac{2 q E L (1 sin θ)}{m})}^{\frac{1}{2}}

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The speed of the particle when the rod is parallel to the electric field is

{(\frac{2 q E L (1 cos θ)}{m})}^{\frac{1}{2}}

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Solution

The correct option is D The speed of the particle when the rod is parallel to the electric field is ${(\frac{2 q E L (1 cos θ)}{m})}^{\frac{1}{2}}$
Since electric field is rightwards A is at highest potential
$V_{A} - V_{B} = (E) (A^{'} B)$

$= E_{l} (1 - cos θ) = E_{l} (1 - cos θ)$

$U_{A} - U_{B} = q (V_{A} - V_{B})$

$= \frac{1}{2} m v^{2} \frac{1}{2} m v_{0}^{2}$

$V_{0} = 0$
$E_{l} (1 - cos θ) (q) = \frac{1}{2} m v^{2}$

$[v = {(\frac{2 q E l (1 cos θ)}{m})}^{\frac{1}{2}}$

For small $θ$ , oscillation is SHM.

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