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Q.

A dipole consisting of two charges +q and -q joined by a massless rod of length ℓ, is seen oscillating with a small amplitude in a uniform electric field of magnitude E. The period of oscillation

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a

is proportional to E

b

is proportional to 1/E

c

is πmℓ3qE

d

is proportional to 1E but ≠πmℓ3qE

answer is C.

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Detailed Solution

I=mℓ212Restoring torque =qEℓsinθ≈qEℓθ=d2θdt2mℓ212∴ω=qEℓI=qEℓ×12 mℓ2=2πT⇒T=πmℓ3qE
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