$A$ rectangular loop of sides $10 \ cm$ and $5 \ cm$ carrying a current $I$ of $12 \ A$ is placed in different orientations as shown in the figures below. If there is a uniform magnetic field of $0.3 \ T$ in the positive $z$ direction,in which orientations would the loop be in $(i)$ stable equilibrium and $(ii)$ unstable equilibrium?

The torque acting on a coil carrying current '$I$',having '$n$' turns and area '$A$',situated parallel to a magnetic field of induction '$B$' is:

$A$ coil in the shape of an equilateral triangle of side $2 \,cm$ is suspended from a vertex such that it hangs in a vertical plane between the poles of a permanent magnet producing a horizontal magnetic field of $100 \times 10^{-3} \,T$. The magnetic field is parallel to the plane of the coil. For the moment of couple acting on the coil to be $2 \sqrt{3} \times 10^{-5} \,Nm$, the current to be passed through the coil is (in $A$)

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

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

$A$ metal wire of length '$L$' is bent to form a circular coil of number of turns '$n$'. The coil is placed in a magnetic field '$B$' and a current '$I$' is passed through the coil. The maximum torque acting on the coil is: