Question 387: Electrostats & Capacitance

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 time period will be given as :
(Consider $$k$$ as Coulomb's constant)

Accepted Answer

$$\begin{aligned}
& \frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{r}}=\mathrm{m} \omega^2 \mathrm{r} \
& \omega^2=\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{mr}^2} \
& \left(\frac{2 \pi}{\mathrm{T}}ight)^2=\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{mr}^2} \
& \mathrm{~T}=2 \pi \mathrm{r} \sqrt{\frac{\mathrm{m}}{2 \mathrm{k} \lambda \mathrm{q}}}
\end{aligned}$$

Answer

$$T^2=\frac{4 \pi^2 m}{2 k \lambda q} r^3$$

Answer

$$T=\frac{1}{2 \pi r} \sqrt{\frac{m}{2 k \lambda q}}$$

Answer

$$T=\frac{1}{2 \pi} \sqrt{\frac{2 k \lambda q}{m}}$$

Answer

$$T=2 \pi r \sqrt{\frac{m}{2 k \lambda q}}$$

Electrostats & Capacitance

A particle of charge '$-q' and mass 'm' moves in a circle of radius 'r' around an infinitely long line charge of linear charge density '+\lambda'. Then time period will be given as : (Consider k$ as Coulomb's constant)

Choose the correct answer: