Due to the flow of current in a circular loop of radius $R$, the magnetic induction produced at the centre of the loop, is $B$. The magnetic moment of the loop is [${\mu }_0=$permeability constant ]

A uniform magnetic field $\overrightarrow{B}$ is directed at an angle of ${45}^{\circ }$ to the $x$- axis, in the $x-y$ plane. $PQRS$ is a square wire frame carrying a steady current $I_0$, with its center at the origin $O$. At time $t=0$, the frame is at rest position, as shown in the figure. The frame is of mass $M$ and length $L$. The torque $\overrightarrow{𝜏}$, about $O$, acting on the frame, due to the magnetic field, is

$P, Q$ and $R$ are long parallel straight wires in air carrying currents as shown. The direction of the resultant force on $R$ is,

The figure shows a wire of arbitrary shape, carrying current $i$ between points $a$ and $b$. The length of the wire is $L$ and the distance between points $a$ and $b$ is $d$. The wire lies in a plane, at right angles to a uniform magnetic field $B$. Then, the force on the wire is

A wire $PQRST$, carrying current $I=5 \mathrm{A}$, is placed in uniform magnetic field $B=2 \mathrm{T}$, as shown in the figure. If the length of part $QR=4 \mathrm{cm}$ and $SR=6 \mathrm{cm}$, then the magnetic force on the edge $SR$ of the wire is