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 $+\lambda$. Then its time period is $\left(\right.$ where $\left.k=\frac{1}{4 \pi \varepsilon_{0}}\right)$

• A. $T=2 \pi r \sqrt{\frac{m}{2 k \lambda q}}$
• B. $T^{2}=\frac{4 \pi^{2} m}{2 k \lambda q}$
• C. $T=\frac{1}{2 \pi r} \sqrt{\frac{2 k \lambda q}{m}}$
• D. $T=\frac{1}{2 \pi r} \sqrt{\frac{m}{2 k \lambda q}}$

Answer 1

Answer: (A)

$\frac{m v^{2}}{r}=q \frac{\lambda}{2 \pi \varepsilon_{0} r} $
$\Rightarrow v=\sqrt{\frac{q \lambda}{2 \pi \varepsilon_{0} m}}=\sqrt{\frac{2 k q \lambda}{m}}$
$T=\frac{2 \pi r}{v}=2 \pi r \sqrt{\frac{m}{2 k q \lambda}}$