Write an expression for the torque acting on a current-carrying loop suspended in a uniform magnetic field.

$A$ 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.

$A$ circular coil carrying a current of $2.5 \ A$ is free to rotate about an axis in its plane perpendicular to an external magnetic field. When the coil is made to oscillate,the time period of oscillation is $T$. If the current through the coil is $10 \ A$,the time period of oscillation is

$A$ current loop in a magnetic field:

$A$ rectangular coil (dimension $5\,cm \times 2\,cm$) with $100\,turns$,carrying a current of $3\,A$ in the clockwise direction,is kept centered at the origin and in the $X-Z$ plane. $A$ magnetic field of $1\,T$ is applied along the $X$-axis. If the coil is tilted through $45^{\circ}$ about the $Z$-axis,then the torque on the coil is.....$Nm$.

$A$ coil in the shape of an equilateral triangle of side $10 \, cm$ lies in a vertical plane between the pole pieces of a permanent magnet producing a horizontal magnetic field of $20 \, mT$. The torque acting on the coil when a current of $0.2 \, A$ is passed through it and its plane becomes parallel to the magnetic field will be $\sqrt{x} \times 10^{-5} \, Nm$. The value of $x$ is ..... .