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JEE Mains · Physics · STD 12 - 1. Electric charges and fields

Two identical positive charges \(Q\) each are fixed at a distance of ' \(2 a\) ' apart from each other. Another point charge qo with mass ' \(m\) ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge \(q_{0}\) executes \(SHM\). The time period of oscillation of charge \(q_{0}\) will be.

  1. A \(\sqrt{\frac{4 \pi^{3} \varepsilon_{0} m a^{3}}{q_{0} Q}}\)
  2. B \(\sqrt{\frac{q_{0} Q}{4 \pi^{3} \varepsilon_{0} m a^{3}}}\)
  3. C \(\sqrt{\frac{2 \pi^{2} \varepsilon_{0} m a^{3}}{q_{0} Q}}\)
  4. D \(\sqrt{\frac{8 \pi^{3} \varepsilon_{0} m \alpha^{3}}{q_{0} Q}}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\sqrt{\frac{4 \pi^{3} \varepsilon_{0} m a^{3}}{q_{0} Q}}\)

Step-by-step Solution

Detailed explanation

\(m \operatorname{acc}^{ n }=\frac{ KQq _{0}[2 a ][2 x ]}{\left( a ^{2}- x ^{2}\right)^{2}}\) \(\Rightarrow \operatorname{acc}^{ n } \approx\left(\frac{4 kQq _{0}}{ ma ^{3}}\right) x\) \(T =2 \pi \sqrt{\frac{\pi \varepsilon_{0} ma ^{3}}{ Qq _{0}}}\)…
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