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

$A$ wire of length $L$ carries a current $i$. If the wire is turned into a circular coil and kept in a uniform magnetic field $B$,the maximum magnitude of torque in the given magnetic field will be

$A$ 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 $\,Nm$)

$A$ coil is placed in $y-z$ plane making an angle of $30^{\circ}$ with the $x$-axis. The current through the coil is $I$,and the number of turns is $N$. If a magnetic field of strength $B$ is applied in the positive $x$-direction,find the torque experienced by the coil (Radius of the coil is $R$).
$(N=100, I=1 \text{ A}, R=2 \text{ m}, B=\frac{1}{\pi} \text{ T})$

$(a)$ $A$ 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 $3000\,G$ is established in the positive $z-$ direction. $A$ rectangular loop of sides $10\,cm$ and $5\,cm$ carries a current of $12\,A$. The loop is placed in the $xy-$ plane as shown in the figure. What is the magnitude of the torque on the loop?