$A$ rectangular coil of $400$ turns and $10^{-2} \ m^2$ area, carrying a current of $0.5 \ A$ is placed in a uniform magnetic field of $1 \ T$ such that the plane of the coil makes an angle of $60^{\circ}$ with the direction of the magnetic field. The initial moment of force acting on the coil in $Nm$ 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 $(\mu_0 = 4\pi \times 10^{-7} \ SI \ units, \pi^2 = 10, \sin 90^{\circ} = 1)$.

$A$ 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 $A$)

The radius of a circular ring of wire is $R$ and it carries a current of $I \, A$. At its centre,a smaller ring of radius $r$ with current $i$ and $N$ turns is placed. Assuming that the planes of the two rings are perpendicular to each other and the magnetic induction produced at the centre of the bigger ring is constant,then the torque acting on the smaller ring will be:

$A$ rectangular loop carrying a current $i$ is placed in a uniform magnetic field $B$. The area enclosed by the loop is $A$. If there are $n$ turns in the loop,the torque acting on the loop is given by

$A$ circular coil of $10$ turns and radius $10 \,cm$ is placed in a uniform magnetic field of $0.1 \,T$ normal to the plane of the coil. If the current in the coil is $5 \,A$, then the magnitude of the torque on the coil is