JEE Mains · Physics · STD 12 - 1. Electric charges and fields
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)
- A \(\mathrm{T}^2=\frac{4 \pi^2 \mathrm{~m}}{2 \mathrm{k} \lambda \mathrm{q}} \mathrm{r}^3\)
- B \(T=2 \pi r \sqrt{\frac{m}{2 k \lambda q}}\)
- C \(\mathrm{T}=\frac{1}{2 \pi \mathrm{r}} \sqrt{\frac{\mathrm{m}}{2 \mathrm{k} \lambda \mathrm{q}}}\)
- D \(\mathrm{T}=\frac{1}{2 \pi} \sqrt{\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{m}}}\)
Answer & Solution
Correct Answer
(B) \(T=2 \pi r \sqrt{\frac{m}{2 k \lambda q}}\)
Step-by-step Solution
Detailed explanation
\(\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{r}}=\mathrm{m} \omega^2 \mathrm{r}\) \(\omega^2=\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{mr}^2}\) \(\left(\frac{2 \pi}{\mathrm{T}}\right)^2=\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{mr}^2}\)…
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