The expression for the torque acting on a coil having area of cross-section $A$,number of turns $n$,placed in a magnetic field of strength $B$,making an angle $\theta$ with the normal to the plane of the coil,when a current $i$ is flowing in it,will be

$A$ uniform magnetic field of $0.3 \text{ T}$ is established along the $+z$-direction. $A$ rectangular loop of sides $10 \text{ cm}$ and $5 \text{ cm}$ carries a current of $12 \text{ A}$ and is placed in the $xy$-plane as shown in the figure. The torque acting on the loop is $....... \text{ Nm}$.

$A$ 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

$A$ 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 $(\mu_0 = 4\pi \times 10^{-7} \ SI \ units, \pi^2 = 10, \sin 90^{\circ} = 1)$.

Two similar wires of equal lengths are bent in the form of a square and a circular loop. They are suspended in a uniform magnetic field and the same current is passed through them. The torque experienced by:

$A$ small coil of $N$ turns has an effective area $A$ and carries a current $I$. It is suspended in a horizontal magnetic field $\overrightarrow{B}$ such that its plane is perpendicular to $\overrightarrow{B}$. The work done in rotating it by $180^\circ$ about the vertical axis is