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)

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Answer & Solution

Correct Answer

(B) \(T=2 \pi r \sqrt{\frac{m}{2 k \lambda q}}\)

Step-by-step Solution

Detailed explanation

\(\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{r}}=\mathrm{m} \omega^2 \mathrm{r}\)

\(\omega^2=\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{mr}^2}\)

\(\left(\frac{2 \pi}{\mathrm{T}}\right)^2=\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{mr}^2}\)

\(\mathrm{~T}=2 \pi \mathrm{r} \sqrt{\frac{\mathrm{m}}{2 \mathrm{k} \lambda \mathrm{q}}}\)

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