$A$ rectangular coil has $2n$ turns,an area $2a$ and carries a current $2I$. The plane of the coil is at $60^{\circ}$ to a horizontal uniform magnetic field of flux density $B$. The torque on the coil due to magnetic force is

$A$ 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 $10^{29}\; m ^{-3}.$)

$A$ rectangular coil $20\,cm \times 20\,cm$ has $100$ turns and carries a current of $1\,A$. It is placed in a uniform magnetic field $B = 0.5\,T$ with the direction of the magnetic field parallel to the plane of the coil. The magnitude of the torque required to hold this coil in this position is ........ $N-m$.

$A$ square loop of side $2a$ carrying current $I$ is kept in the $xz$-plane with its centre at the origin. $A$ long wire carrying the same current $I$ is placed parallel to the $z$-axis and passes through the point $(0, b, 0)$,where $b \gg a$. The magnitude of the torque on the loop about the $z$-axis is:

The torque required to hold a small circular coil of $10$ turns,$2 \times 10^{-4} \ m^2$ area,and carrying $0.5 \ A$ current in the middle of a long solenoid of $10^3$ turns per meter carrying $3 \ A$ current,with its axis perpendicular to the axis of the solenoid,is:

$A$ square loop of side $2a$ carrying current $I$ is kept in the $XZ$ plane with its centre at the origin. $A$ long wire carrying the same current $I$ is placed parallel to the $z$-axis and passes through the point $(0, b, 0)$,where $b >> a$. The magnitude of the torque on the loop about the $z$-axis is given by: