The figure shows four orientation of an electric dipole in an external electric field. The correct ranking of the magnitude of the torque and the potential energy of the dipole is
(a) τ 1 = τ 3 > τ 2 = τ 4 and U1 = U2 = U3 = U4
(b) τ 1 > τ 2 = τ 3 > τ 4 and U1 > U2 = U3 > U4
(c) τ 1 = τ 2 > τ 3 = τ 4 and U2 = U4 > U1 = U3
(d) τ 1 = τ 2 = τ 3 = τ 4 and U1 = U3 > U2 = U4
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(d) τ 1 = τ 2 = τ 3 = τ 4 and U1 = U3 > U2 = U4
Explanation:
For 2 and 4, τ = pEsinθ and U = −pEcosθ.
For 1 and 3, τ = pEsin(180−θ) = pEsinθ. So U = −pEcos(180−θ) = pEcosθ
So we find that τ 1 = τ 2 = τ 3 = τ 4 meaning torque is same for all.
U is greater for 1 and 3 than 2 and 4.
U1 = U3 > U2 = U4
Option D is the answer.
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