$A$ magnetic dipole with magnetic moment $p_m$ is placed parallel to an infinitely long straight wire carrying current $I$,as shown in the figure. Which of the following statements is correct?

$A$ circular coil having $200$ turns,$2.5 \times 10^{-4} \text{ m}^2$ area and carrying $100 \mu\text{A}$ current is placed in a uniform magnetic field of $1 \text{ T}$. Initially,the magnetic dipole moment $(\vec{M})$ was directed along $\vec{B}$. The amount of work required to rotate the coil through $90^{\circ}$ from its initial orientation such that $\vec{M}$ becomes perpendicular to $\vec{B}$ is . . . . $\mu\text{J}$.

$A$ 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.

$A$ uniform magnetic field $B$ of $0.3\, T$ is along the positive $Z-$ direction. $A$ rectangular loop $(abcd)$ of sides $10\, cm \times 5\, cm$ carries a current $I$ of $12\, A$. Out of the following different orientations,which one corresponds to stable equilibrium?

$A$ rectangular loop carrying a current $i$ is placed in a uniform magnetic field $B$. The area enclosed by the loop is $A$. If there are $n$ turns in the loop,the torque acting on the loop is given by

$A$ triangular loop of side $l$ carries a current $I$. It is placed in a magnetic field $B$ such that the plane of the loop is in the direction of $B$. The torque on the loop is