Question

A particle of charge $- q \&$ mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear charge density $+\lambda$. Then time period will be : $\left[ K =\frac{1}{4 \pi \varepsilon_{0}}\right]$

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

Answer 1

Answer: (A)

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