An electric dipole of moment P→ is placed in a uniform electric field E→ such that P→ points alongE→. If the dipole is slightly rotated about an axis perpendicular to the plane containing E→ and P→ and passing through the centre of the dipole, the dipole executes simple harmonic motion. Consider I to be the moment of inertia of the dipole about the axis of rotation. What is the time period of such oscillation
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a
(PE/I)
b
2π(I/pE).
c
2π(I/2pE)
d
None of these
answer is B.
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Detailed Solution
The dipole experiences a torque pE sinθ tending to bring itself back in the direction of field. Therefore, on being released (i.e.rotated) he dipole oscillates about an axis through its centre of mass and perpendicular to the field. If I is the moment then the equation of motion isI.d2θ/dt2=−PEsinθFor small amplitude sinθ≈θThis is a S.H.M., whose period of oscillation is T=2π/ω=2π(I/PE).