$A$ circular coil of $30$ turns and radius $8 \,cm$ carrying a current of $6 \,A$ is suspended vertically in a uniform horizontal magnetic field of magnitude $1.0 \,T$. The field lines make an angle of $20^{\circ}$ with the normal of the coil. The magnitude of the counter torque that must be applied to prevent the coil from turning is (in $\,Nm$)

Current $I$ is carried in a wire of length $L$. If the wire is bent into a circular coil of single turn,the maximum torque in a given magnetic field $B$ is:

$A$ 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

$A$ wire of length $L$ is bent in the form of a circular coil and current $i$ is passed through it. This coil is kept in a magnetic field. The torque acting on the coil will be maximum, when the number of turns is . . . . . .

$A$ solenoid of length $0.4 \ m$ and having $500$ turns of wire carries a current $3 \ A$. $A$ thin coil having $10$ turns of wire and radius $0.1 \ m$ carries current $0.4 \ A$. The torque required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid is $(\mu_0 = 4\pi \times 10^{-7} \ SI \ units, \pi^2 = 10, \sin 90^{\circ} = 1)$.

$A$ uniform magnetic field of $0.3 \; T$ is established along the positive $Z$-direction. $A$ rectangular loop in the $XY$-plane with sides $10 \; cm$ and $5 \; cm$ carries a current of $I = 12 \; A$ as shown. The torque on the loop is