$A$ 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 ........ $J$.

In the figure shown,a coil of single turn is wound on a sphere of radius $R$ and mass $m$. The plane of the coil is parallel to the inclined plane and lies in the equatorial plane of the sphere. The current in the coil is $i$. If the sphere is in equilibrium,the value of the magnetic field $B$ is:

$A$ current-carrying coil is subjected to a uniform magnetic field. The coil will orient itself so that its plane becomes

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

$A$ thin wire of length $L$ made of an insulating material is bent to form a circular loop and a positive charge $q$ is given so that it is distributed uniformly around the circumference of the loop. The loop is then rotated with an angular speed $\omega$ about an axis passing through its centre. If a uniform magnetic field $B$ directed parallel to the plane of the loop is applied,then the magnitude of the magnetic torque on the loop is:

$A$ single circular loop of radius $1.00 \, m$ carries a current of $10.0 \, mA$. It is placed in a uniform magnetic field of magnitude $0.500 \, T$ that is directed parallel to the plane of the loop as shown in the figure. The magnitude of the torque exerted on the loop by the magnetic field is: