# A particle of charge -q and mass m moves in a circle of radius r arround an infinitely long line charge of linear density $\;+\lambda\;$ . Then time period will be

$(a)\;2 \pi r \sqrt{\large\frac{m}{2 k \lambda q}}\qquad(b)\;2 \pi \sqrt{\large\frac{m r^3}{2 k \lambda q}}\qquad(c)\;\large\frac{1}{2 \pi r}\;\sqrt{\large\frac{2 k \lambda q}{m}}\qquad(d)\;\large\frac{1}{2 \pi r}\;\sqrt{\large\frac{m}{2 k \lambda q}}$

Answer : (a) $\;2 \pi r \sqrt{\large\frac{m}{2 k \lambda q}}$
Explanation :
Centripetal force = Eq
$=\large\frac{2\;k\;\lambda\;q}{r}$
$\large\frac{2\;k\;\lambda\;q}{r}=\large\frac{mv^2}{r}$
$v=\sqrt{\large\frac{2\;k\;\lambda\;q}{m}}$
$T=\large\frac{2 \pi r}{v}=2 \pi r \sqrt{\large\frac{m}{2\;k\;\lambda\;q}}\;.$