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 \(W = -pE(\cos 60^\circ - \cos 30^\circ) = pE(\cos 30^\circ - \cos 60^\circ) = 2\tau(\frac{\sqrt{3}}{2} - \frac{1}{2}) = (\sqrt{3}-1)\tau\).

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. A point Q lies on the perpendicular bisector of an electric dipole of dipole moment p. If the distance of Q from the dipole is r (much larger than the size of the dipole) then electric field at Q is proportional to :
2. 9. Point charges $+4q$, $-q$ and $+4q$ are kept on the X-axis at point $x = 0$, $x = a$ and $x = 2a$ respectively. (1988)
3. The electrostatic potential on the surface of a charged solid conducting sphere is \( 100 \text{ volts} \). Two statements are made in this regard : Assertion (A): At any point inside the sphere, electrostatic potential is \( 100 \text{ volt} \). Reason (R): At any point inside the sphere, electric field is zero.  
4. Assertion (A): We can shield a charge from electric fields by putting it inside a hollow conductor but we can not shield a body from the gravitational influence of near by matter by putting it inside a hollow sphere. Reason (R): Gravitational force in between two point mass bodies is independent of the intervening medium them.  
5. An electric dipole with dipole moment \( 2\times 10^{-9} \)Cm is aligned at 30ยบ with the direction of a uniform electric field of magnitude \( 4\times 10^{4} NC^{-1}\). The magnitude of the torque acting on the dipole is :