Work done on a dipole – Rankers Physics

Electric Dipole: Practice Problem & Solution

An electric dipole is placed in a uniform electric field making an angle \(30^\circ\) with electric field and it experiences torque equal to \(\tau\) in this scenario. The minimum work done in changing the orientation from \(30^\circ\) to \(60^\circ\) is equal to
\((\sqrt{3}-1)\tau\)
\(\frac{(\sqrt{3}-1)\tau}{2}\)
\((\sqrt{3}+1)\tau\)
\(\frac{(\sqrt{3}+1)\tau}{2}\)

Solution Explained:

To solve this problem, we apply the core principles of Electric Dipole. Understanding the underlying formula is key to arriving at the correct answer below:

Torque is \(\tau = pE \sin 30^\circ = pE/2 \implies pE = 2\tau\). Work done is \(W = -pE(\cos 60^\circ - \cos 30^\circ) = pE(\cos 30^\circ - \cos 60^\circ) = 2\tau(\frac{\sqrt{3}}{2} - \frac{1}{2}) = (\sqrt{3}-1)\tau\).

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