Electrostatics Question 14
Question 14 - 2024 (30 Jan Shift 2)
A particle of charge ’ $-q$ ’ and mass ’ $m$ ’ moves in a circle of radius ’ $r$ ’ around an infinitely long line charge of linear density ’ $+\lambda$ ‘. Then time period will be given as:
(Consider $k$ as Coulomb’s constant)
(1) $T^{2}=\frac{4 \pi^{2} m}{2 k \lambda q} r^{3}$
(2) $T=2 \pi r \sqrt{\frac{m}{2 k \lambda q}}$
(3) $T=\frac{1}{2 \pi r} \sqrt{\frac{m}{2 k \lambda q}}$
(4) $T=\frac{1}{2 \pi} \sqrt{\frac{2 k \lambda q}{m}}$
Show Answer
Answer: (2)
$\frac{2 k \lambda q}{r}=m \omega^{2} r$
$\omega^{2}=\frac{2 k \lambda q}{mr^{2}}$
$\left(\frac{2 \pi}{T}\right)^{2}=\frac{2 k \lambda q}{mr^{2}}$
$T=2 \pi r \sqrt{\frac{m}{2 k \lambda q}}$
