Current $i$ is carried in a wire of length $L$. If the wire is turned into a circular coil,the maximum magnitude of torque in a given magnetic field $B$ will be

$(a)$ $A$ circular coil of $30$ turns and radius $8.0 \; cm$ carrying a current of $6.0 \; A$ is suspended vertically in a uniform horizontal magnetic field of magnitude $1.0 \; T$. The field lines make an angle of $60^{\circ}$ with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning.
$(b)$ Would your answer change,if the circular coil in $(a)$ were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)

$A$ 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 $....... \text{ Nm}$.

$A$ current-carrying loop is free to turn in a uniform magnetic field. The loop will come into equilibrium when its plane is inclined at

$A$ rectangular conducting loop consists of two wires on two opposite sides of length $l$ joined together by rods of length $d$. The wires are each of the same material but with cross-sections differing by a factor of $2$. The thicker wire has a resistance $R$ and the rods are of low resistance,which in turn are connected to a constant voltage source $V_{0}$. The loop is placed in a uniform magnetic field $\vec{B}$ at $45^{\circ}$ to its plane. Find the torque exerted by the magnetic field on the loop about an axis through the centers of the rods.

The $(\tau - \theta)$ graph for a current-carrying coil in a magnetic field is: