A bar magnet of magnetic moment $1.5~\text{J/T}$ lies aligned with the direction of a uniform magnetic field of $0.22~\text{T}$. What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment normal to the field direction?
1. $0.66$ J
2. $0.33$ J
3. $0$
4. $0.44$ J

A circular coil of $16$ turns and a radius of $10~\text{cm}$ carrying a current of $0.75~\text{A}$ rests with its plane normal to an external field of magnitude $5.0\times 10^{-2}~\text{T}$. The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a frequency of $2.0~\text{s}^{-1}$${\mathrm{}}^{}.$The moment of inertia of the coil about its axis of rotation is:
1. $1.39\times 10^{-4}~ \text{kg m}^{2}$
2. $2.19\times 10^{-4} ~\text{kg m}^{2}$
3. $2.39\times 10^{-4} ~\text{kg m}^{2}$
4. $1.19\times 10^{-4}~\text{kg m}^{2}$

A Rowland ring of mean radius $15$ cm has $3500$ turns of wire wound on a ferromagnetic core of relative permeability $800.$ What is the magnetic field $B$ in the core for a magnetizing current of $1.2$ A?
1. $3.27$ T
2. $2.56$ T
3. $1.05$ T
4. $4.48$ T