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QJEEM23Ph0bc2: JEE Main 2023 Physics - Class 12 JEEM23Ph0bc2 Solution: A dipole comprises of two charged particles of identical…

A dipole comprises of two charged particles of identical magnitude qq and opposite in nature. The mass 'm' of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance ' ll '. If the dipole is placed in a uniform electric field ' Eˉ\bar{E} '; in such a way that dipole axis makes a very small angle with the electric field, ' Eˉ\bar{E} '. The angular frequency of the oscillations of the dipole when released is given by:

Multiple Choice Options

  • A 3qE2ml\sqrt{\frac{3 q E}{2 m l}}
  • B 4qEml\sqrt{\frac{4 q E}{m l}}
  • C 8qE3ml\sqrt{\frac{8 q E}{3 m l}}
  • D 8qEml\sqrt{\frac{8 q E}{m l}}

Step-by-Step Verified Solution

JEE Main 2023 (Online) 6th April Evening Shift Physics - Electrostatics Question 51 English Explanation
If released, it will oscillate about centre of mass.

For small ' θ\theta '

amp;τ=−PE.θamp;⇒[2 m129+m4l29]α=−qlE⋅θamp;⇒2ml23α=−qlE⋅θ⇒α=−3qE2mlθamp;ω=3qE2ml\begin{aligned}& \tau=-\mathrm{PE} . \theta \\\\& \Rightarrow\left[2 \mathrm{~m} \frac{1^2}{9}+\mathrm{m} \frac{4 \mathrm{l}^2}{9}\right] \alpha=-\mathrm{qlE} \cdot \theta \\\\& \Rightarrow \frac{2 \mathrm{ml}^2}{3} \alpha=-\mathrm{qlE} \cdot \theta \Rightarrow \alpha=-\frac{3 \mathrm{qE}}{2 \mathrm{ml}} \theta \\\\& \omega=\sqrt{\frac{3 \mathrm{qE}}{2 \mathrm{ml}}}\end{aligned}

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