$A$ thin magnetic needle is placed in a magnetic field of $200 \ G$ with its axis at $30^{\circ}$ to the direction of the field. Find the magnetic moment of the needle if it experiences a torque of $0.012 \ Nm$ in this field. (in $Am^2$)

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:

$A$ current-carrying coil experiences a torque due to a magnetic field. The value of the torque is $80 \%$ of the maximum possible torque. The angle between the magnetic field and the normal to the plane of the coil is

$A$ single circular loop of radius $1.00 \, m$ carries a current of $10.0 \, mA$. It is placed in a uniform magnetic field of magnitude $0.500 \, T$ that is directed parallel to the plane of the loop as shown in the figure. The magnitude of the torque exerted on the loop by the magnetic field is:

$A$ circular coil of radius $10 \,cm$ with $100$ turns carrying a current of $0.5 \,A$ lies in a magnetic field of $2 \,T$ such that the normal drawn to the plane of the coil makes an angle $\theta$ with the direction of the field. Work done in rotating the coil to change the angle $\theta$ from $0^{\circ}$ to $180^{\circ}$ is

$A$ 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 $\text{ rad/s}$)?