The torque required to hold a small circular coil of $10$ turns,$2 \times 10^{-4} \ m^2$ area,and carrying $0.5 \ A$ current in the middle of a long solenoid of $10^3$ turns per meter carrying $3 \ A$ current,with its axis perpendicular to the axis of the solenoid,is:

$A$ 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?

$A$ circular coil of $20$ turns and radius $10\, cm$ is placed in a uniform magnetic field of $0.10\, T$ normal to the plane of the coil. If the current in the coil is $5\, A$,then the torque acting on the coil will be...... $Nm$.

$A$ coil having $10 \text{ A m}^2$ magnetic moment is placed in a vertical plane and is free to rotate about its horizontal axis, which coincides with its diameter. $A$ uniform magnetic field of $2 \text{ T}$ in the horizontal direction exists such that initially the axis of the coil is in the direction of the field. The coil rotates through an angle of $90^{\circ}$ under the influence of the magnetic field. The moment of inertia of the coil is $0.1 \text{ kg m}^2$. What will be its angular speed (in $\text{ rad/s}$)?

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

$A$ rectangular coil of length $0.12\, m$ and width $0.1\, m$ having $50$ turns of wire is suspended vertically in a uniform magnetic field of strength $0.2\, Wb/m^2$. The coil carries a current of $2\, A$. If the plane of the coil is inclined at an angle of $30^{\circ}$ with the direction of the field,the torque required to keep the coil in this position will be .......$Nm$.