$A$ circular current loop of magnetic moment $M$ is in an arbitrary orientation in an external uniform magnetic field $\vec{B}$. The work done to rotate the loop by $30^{\circ}$ about an axis perpendicular to its plane is

$A$ uniform magnetic field of $3000\,G$ is established in the positive $z-$ direction. $A$ rectangular loop of sides $10\,cm$ and $5\,cm$ carries a current of $12\,A$. The loop is placed in the $xy-$ plane as shown in the figure. What is the magnitude of the torque on the loop?

$A$ current $i$ flows in a circular coil of radius $r$. If the coil is placed in a uniform magnetic field $B$ with its plane parallel to the field,the magnitude of the torque that acts on the coil is

Suppose we want to verify the analogy between electrostatic and magnetostatic by an explicit experiment. Consider the motion of
$(i)$ electric dipole $\vec{p}$ in an electrostatic field $\vec{E}$ and
$(ii)$ magnetic dipole $\vec{M}$ in a magnetic field $\vec{B}$. Write down a set of conditions on $\vec{E}, \vec{B}, \vec{p}, \vec{M}$ so that the two motions are verified to be identical. (Assume identical initial conditions.)

$A$ coil is placed in $y-z$ plane making an angle of $30^{\circ}$ with the $x$-axis. The current through the coil is $I$,and the number of turns is $N$. If a magnetic field of strength $B$ is applied in the positive $x$-direction,find the torque experienced by the coil (Radius of the coil is $R$).
$(N=100, I=1 \text{ A}, R=2 \text{ m}, B=\frac{1}{\pi} \text{ T})$

$A$ current-carrying rectangular coil is placed in a uniform magnetic field. In which orientation will the coil not tend to rotate?