$A$ $250$-turn rectangular coil of length $2.1\, cm$ and width $1.25\, cm$ carries a current of $85\, \mu A$ and is subjected to a magnetic field of strength $0.85\, T.$ The work done to rotate the coil by $180^o$ against the torque is .............. $\mu J$.

$A$ thin non-conducting disc of radius $R$ is rotating clockwise (see figure) with an angular velocity $\omega$ about its central axis,which is perpendicular to its plane. Both its surfaces carry positive charges of uniform surface density. Half the disc is in a region of a uniform,unidirectional magnetic field $B$ parallel to the plane of the disc,as shown. Then,

$A$ 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 ........ $N-m$.

Four wires each of length $2.0 \, m$ are bent into four loops $P$,$Q$,$R$ (labeled as $P$ in the image,but distinct),and $S$ and then suspended in a uniform magnetic field. The same current is passed through each loop. Which statement is correct?

$A$ circular coil of radius $2 \text{ cm}$ and $125 \text{ turns}$ carries a current of $1 \text{ A}$. The coil is placed in a uniform magnetic field of magnitude $0.4 \text{ T}$. The axis of the coil makes an angle of $30^{\circ}$ with the direction of the magnetic field. The torque acting on the coil is $\alpha \times 10^{-4} \text{ N.m}$. The value of $\alpha$ is . . . . . . .

Four wires,each of length $2.0\,m$,are bent into four loops $P, Q, R$ and $S$ and then suspended in a uniform magnetic field. If the same current is passed in each,then the torque will be maximum on the loop: