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Question

# An electric dipole is placed along the x-axis at the origin O. A point P is at a distance of 20cm from this origin such that OP makes an angle π/3 with the x-axis. If the electric field at P makes an angle θ with the x-axis, the value of θ would be :

A
π3
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B
π3+tan1(32)
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C
2π3
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D
tan1(32)
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Solution

## The correct option is B π3+tan−1(√32)The electric potential at P due to dipole is V=kpcosϕr2 where p be the dipole moment and k=14πϵ0Here, Er=−∂V∂r=k2pcosϕr3 and Eϕ=−1r∂V∂ϕ=kpsinϕr3From figure, tanα=EϕEr=12tanϕ=12tanπ3 (as ϕ=π/3)or α=tan−1(√32)Thus, the angle θ=ϕ+α=π3+tan−1(√32)

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