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Question

An electric dipole has a fixed dipole moment p, which makes angle θ with respect to x axis. When system is subjected to an electric field E1=E ^i, it experiences a torque τ1=τ ^k. When subjected to another electric field E2=3E ^j, it experiences a torque τ2=τ1. The angle θ is

A
90
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B
30
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C
60
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D
45
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Solution

The correct option is C 60
Given:
E1=E ^i; E2=3E ^j

τ1=τ ^k; τ2=τ1


We know that torque on a dipole in a uniform electric field is

τ=p×E

So, when electric field E1=E ^i is applied, then torque,

τ1=p×E1

τ ^k=p×E ^i=pEsinθ ^k

τ=pEsinθ ........(1)

Now, when electric field, E2=3E ^j applied then torque,

τ2=p×E2

τ1=τ^k=3pEsin(90θ) ^k

τ=3pEcosθ .........(2)

From eqs.(1) and (2)

pEsinθ=3pEcosθ

tanθ=3

θ=60

Hence, option (b) is the correct answer.

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