Question

A particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear charge density $+\lambda$. The speed of particle is

• A. $\sqrt{\frac{5k\lambda q}{m}}$
• B. $\sqrt{\frac{2k\lambda q}{m}}$
• C. $\sqrt{\frac{k\lambda q}{m}}$
• D. $\sqrt{\frac{3k\lambda q}{m}}$

Answer 1

The correct option is B $\sqrt{\frac{2k\lambda q}{m}}$

Let $v$ be the speed of particle moving in the circle.

Here, the electric force $\left(F_e\right)$ acting on charge $-q$ due to infinite line charge will act as the required centripetal force.

So, $F_e=\frac{m{v}^2}{r}$

$\Rightarrow qE=\frac{m{v}^2}{r}$

$\Rightarrow q\times \frac{2k\lambda }{r}=\frac{m{v}^2}{r}[\because E=\frac{2k\lambda }{r}]$

$\Rightarrow v=\sqrt{\frac{2k\lambda q}{m}}$

Hence, option $\left(b\right)$ is the correct answer.