Magnetic Dipole — MCQ Practice

A circular coil of radius $R$ and $N$ turns carries a current $I$. It is placed in a uniform magnetic field $B$. If the magnetic dipole moment of the coil is $\vec{m}$, and the torque experienced by the coil is $\vec{\tau}$, which of the following statements is correct?

A bar magnet of magnetic moment $1.5,\text{A m}^2$ is placed in a uniform magnetic field of $0.2,\text{T}$. If the magnet is initially aligned parallel to the field, what is the work done to rotate it by $60^circ$?

A current loop of area $0.1,\text{m}^2$ carrying a current of $2,\text{A}$ is placed in a uniform magnetic field of $0.5,\text{T}$. If the plane of the loop is at an angle of $30^circ$ to the magnetic field, what is the magnitude of the torque acting on the loop?

A magnetic dipole of moment $\vec{m} = (3\hat{i} + 4\hat{j}),\text{A m}^2$ is placed in a uniform magnetic field $\vec{B} = (2\hat{i} - 3\hat{k}),\text{T}$. What is the torque experienced by the dipole?

An electron in a hydrogen atom orbits the nucleus in a circular path of radius $0.53 \times 10^{-10},\text{m}$ with a speed of $2.2 \times 10^6,\text{m/s}$. What is the magnitude of the orbital magnetic dipole moment of the electron? (Charge of electron $e = 1.6 \times 10^{-19},\text{C}$)

A magnetic dipole is oriented such that its potential energy in a uniform magnetic field is maximum. If it is then rotated to the position of minimum potential energy, what is the work done by the magnetic field?

Which of the following statements is INCORRECT regarding a magnetic dipole in a uniform magnetic field?