$A$ square loop of length $L$ is placed with its edges parallel to the $XY$-axes. The loop carries a current $I$. If the magnetic field in the region varies as $B = B_0 \left(1 + \frac{xy}{L^2}\right) \hat{k}$,then the magnitude of the net force on the loop will be:

Two long conductors separated by a distance $d$ carry currents $I_1$ and $I_2$ in the same direction. They exert a force $F$ on each other. Now,the current in one of them is increased to $2$ times and its direction is reversed. The distance between them is also increased to $3d$. The new value of force between them is:

The force per unit length on a straight wire carrying a current of $8 \ A$ making an angle of $30^{\circ}$ with a uniform magnetic field of $0.15 \ T$ is: (in $N \ m^{-1}$)

$A$ rectangular loop of wire,supporting a mass $m$,hangs with one end in a uniform magnetic field $\vec B$ pointing into the plane of the paper. $A$ clockwise current $i$ is set up such that $i > mg/Ba$,where $a$ is the width of the loop. Then:

$A$ current-carrying rectangular loop $PQRS$ is made of uniform wire. The lengths are $PR = QS = 5\,cm$ and $PQ = RS = 100\,cm$. If the ammeter current reading changes from $I$ to $2I$,the ratio of magnetic forces per unit length on the wire $PQ$ due to wire $RS$ in the two cases respectively,$f_{PQ}^{I} : f_{PQ}^{2I}$,is:

The magnetic field existing in a region is given by $\vec{B} = 0.2(1 + 2x) \hat{k} \text{ T}$. $A$ square loop of edge $50 \text{ cm}$ carrying $0.5 \text{ A}$ current is placed in the $x-y$ plane with its edges parallel to the $x-y$ axes,as shown in the figure. The magnitude of the net magnetic force experienced by the loop is . . . . . . $\text{mN}$.