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Question

An electric dipole is made up of two particles, one having charge +1 μC and mass 1 kg and the other with charge 1 μC and mass 1 kg separated by distance 1 m. It is in equilibrium in a uniform electric field of 20×103 V/m. If the dipole is deflected through an angle 2, then time taken by it to come again at equilibrium position is

A
2π s
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B
2.5π s
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C
4 s
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D
5 s
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Solution

The correct option is B 2.5π s
The moment of inertia of the system about an axis through the centre of the dipole is,
I=2(md2)=2×1×(12)2=12 kg-m2

Also, dipole moment,

p=q(2r)=106×1=106 C-m

Given: E=20×103 V/m

As the system is rotated through a very small angle from equilibrium position, the resulting motion will be an oscillation.

Hence, the time period will be,

T=2πIpE=2π1/2106×20×103

T=10π

So, time taken to come to equilibrium position from the extreme position directly is,

t=T4=10π4=2.5π s
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