Verified Solution • 2025–26 Session moderate

QJEEM25Phd1c2: JEE Main 2025 Physics - Class 12 JEEM25Phd1c2 Solution: An electric dipole of mass , charge , and length is placed in a …

An electric dipole of mass mm , charge qq , and length ll is placed in a uniform electric field E⃗=E0i^\vec{E} = E_0\hat{i} . When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be :

Multiple Choice Options

  • A 12πml2qE0\frac{1}{2\pi} \sqrt{\frac{ml}{2qE_0}}
  • B 2πml2qE02\pi \sqrt{\frac{ml}{2qE_0}}
  • C 2πmlqE02\pi \sqrt{\frac{ml}{qE_0}}
  • D 12π2 mlqE0\frac{1}{2 \pi} \sqrt{\frac{2 \mathrm{~m} l}{\mathrm{q} \mathrm{E}_0}}

Step-by-Step Verified Solution

amp;Iω2θ=qℓE0θamp;2 m(ℓ2)2ω2=qℓE0amp;ω2=2qE0 mℓamp; T=2π mℓ2qE0\begin{aligned}& \mathrm{I} \omega 2 \theta=\mathrm{q} \ell \mathrm{E}_0 \theta \\& 2 \mathrm{~m}\left(\frac{\ell}{2}\right)^2 \omega^2=\mathrm{q} \ell \mathrm{E}_0 \\& \omega^2=\frac{2 \mathrm{qE}_0}{\mathrm{~m} \ell} \\& \mathrm{~T}=2 \pi \sqrt{\frac{\mathrm{~m} \ell}{2 \mathrm{qE}_0}}\end{aligned}

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