$A$ $100$ turns coil shown in the figure carries a current of $2\, A$ in a magnetic field $B = 0.2\, Wb/m^2$. The torque acting on the coil is

$A$ circular coil of radius $4\, cm$ has $50$ turns. In this coil,a current of $2\, A$ is flowing. It is placed in a magnetic field of $0.1\, Wb/m^2$. The amount of work done in rotating it through $180^\circ$ from its equilibrium position will be ........ $J$.

$A$ metal wire of length '$L$' is bent to form a circular coil of number of turns '$n$'. The coil is placed in a magnetic field '$B$' and a current '$I$' is passed through the coil. The maximum torque acting on the coil is:

$A$ uniform,constant magnetic field $\vec B$ is directed at an angle of $45^o$ to the $x-$ axis in the $xy-$ plane. $PQRS$ is a rigid square wire frame carrying a steady current $I_0,$ with its centre at the origin $O.$ At time $t = 0,$ the frame is at rest in the position shown in the figure,with its sides parallel to the $x$ and $y$ axis. Each side of the frame is of mass $M$ and length $L.$ Find the torque $\vec \tau$ acting on the frame.

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

$A$ current-carrying coil experiences a torque due to a magnetic field. The value of the torque is $80 \%$ of the maximum possible torque. The angle between the magnetic field and the normal to the plane of the coil is