$A$ galvanometer coil has $500$ turns and each turn has an average area of $3 \times 10^{-4} \ m^{2}$. If a torque of $1.5 \ Nm$ is required to keep this coil parallel to the magnetic field when a current of $0.5 \ A$ is flowing through it,the strength of the magnetic field (in $T$) is:

Current $i$ is carried in a wire of length $L$. If the wire is turned into a circular coil,the maximum magnitude of torque in a given magnetic field $B$ will be

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.)

$A$ rectangular loop of sides $10 \ cm$ and $5 \ cm$ carrying a current $I$ of $12 \ A$ is placed in different orientations as shown in the figures below. If there is a uniform magnetic field of $0.3 \ T$ in the positive $z$ direction,in which orientations would the loop be in $(i)$ stable equilibrium and $(ii)$ unstable equilibrium?

$A$ thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass $m$ and radius $r$ and it is in a uniform vertical magnetic field $B_0$,as shown in the figure. Initially,it hangs vertically downwards,because of acceleration due to gravity $g$,on two conducting supports at $P$ and $Q$. When a current $I$ is passed through the loop,the loop turns about the line $PQ$ by an angle $\theta$ given by

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