$A$ rectangular coil of length $0.12\, m$ and width $0.1\, m$ having $50$ turns of wire is suspended vertically in a uniform magnetic field of strength $0.2\, Wb/m^2$. The coil carries a current of $2\, A$. If the plane of the coil is inclined at an angle of $30^{\circ}$ with the direction of the field,the torque required to keep the coil in this position will be .......$Nm$.

$A$ square loop of side $l$ is kept in a uniform magnetic field $B$ such that its plane makes an angle $\alpha$ with $\vec{B}$. The loop carries a current $i$. The torque experienced by the loop in this position is

$A$ coil in the shape of an equilateral triangle of side $2 \,cm$ is suspended from a vertex such that it hangs in a vertical plane between the poles of a permanent magnet producing a horizontal magnetic field of $100 \times 10^{-3} \,T$. The magnetic field is parallel to the plane of the coil. For the moment of couple acting on the coil to be $2 \sqrt{3} \times 10^{-5} \,Nm$, the current to be passed through the coil is (in $A$)

$A$ current loop in a magnetic field:

Four wires of equal length are bent in the form of four loops $P, Q, R$ and $S.$ These are suspended in a uniform magnetic field and the same current is passed through them. The maximum torque will act on:

The torque required to hold a small circular coil of $10$ turns, area $1 \,mm^{2}$ and carrying a current of $\left(\frac{21}{44}\right) \,A$ in the middle of a long solenoid of $10^{3} \,turns/m$ carrying a current of $2.5 \,A$, with its axis perpendicular to the axis of the solenoid is