In finding the potential energy of a magnetic dipole in a uniform magnetic field, the constant of integration is taken as zero. With this choice, the potential energy of the dipole is zero when the angle between its magnetic moment and the field is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(90^\circ\)
The potential energy is found by integrating the torque \( \tau=mB\sin\theta \) over the angle. The zero of potential energy can be fixed at any convenient position. With the constant of integration taken as zero, \( U_m=-mB\cos\theta \). This energy is zero where \( \cos\theta \) is zero.
\( \begin{aligned} -mB\cos\theta &= 0 \\ \cos\theta &= 0 \\ \theta &= 90^\circ \end{aligned} \)
At this angle the dipole is perpendicular to the field.
NCERT (2026-27):
The dipole in a uniform magnetic field – “The magnetic potential energy Um is given by”
\( U_m=\int\tau(\theta)d\theta=\int mB\sin\theta\,d\theta= \)\( -mB\cos\theta \)\( =-\mathbf{m}\cdot\mathbf{B} \qquad (5.3) \)
“We have emphasised in Chapter 2 that the zero of potential energy can be fixed at one’s convenience. Taking the constant of integration to be zero means fixing the zero of potential energy at θ = 90°, i.e., when the needle is perpendicular to the field. …”