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Question

An electric dipole of dipole moment p is placed in a uniform electric field E in stable equilibrium position. Its moment of inertia about the centroidal axis is I. If it is displaced slightly from its mean position, find the period of small oscillations.

A
2πIpE
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B
12πpEI
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C
πIpE
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D
2πIEp
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Solution

The correct option is A 2πIpE

When the dipole displaced at an angle θ from its mean position, the magnitude of restoring torque will be

τ=pEsinθ...(1)

For very small angular displacement,
sinθθ

From equation (1),

τ=pEθ

We know that, the angular acceleration is
α=τI

Substituting the value of τ in the above expression,
α=(pEi)θ=ω2θ
where, ω is angular frequncy of the oscillation,

Therefore,
ω2=pEI

So, time period, T of oscillation,

T=2πω=2πIpE

Hence, option (a) is correct answer.

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