$A$ 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

The $(\tau - \theta)$ graph for a current-carrying coil in a magnetic field is:

$A$ coil having $100$ turns, area of $5 \times 10^{-3} \, m^2$, carrying current of $1 \, mA$ is placed in a uniform magnetic field of $0.20 \, T$ such that the plane of the coil is perpendicular to the magnetic field. The work done in turning the coil through $90^{\circ}$ is . . . . . . $\mu J$.

$A$ circular loop of radius $R$ carries a current $I$. Another circular loop of radius $r (r \ll R)$ carries a current $i$ and is placed at the centre of the larger loop. The planes of the two circles are at right angles to each other. Find the torque acting on the smaller loop.

$A$ circular coil of $20$ turns and radius $10\; cm$ is placed in a uniform magnetic field of $0.10\; T$ normal to the plane of the coil. If the current in the coil is $5.0\; A$,what is the
$(a)$ total torque on the coil,
$(b)$ total force on the coil,
$(c)$ average force on each electron in the coil due to the magnetic field?
(The coil is made of copper wire of cross-sectional area $10^{-5} \;m ^{2},$ and the free electron density in copper is given to be about $10^{29}\; m ^{-3}.$)

$A$ circular coil having $N$ turns and radius $R$ carrying current $I$ is held in the $z-x$ plane in a magnetic field $B\hat{k}$. The torque on the coil due to the magnetic field in $N-m$ is: