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 . . . . . . $\text{mN}$.

The force acting on a current-carrying wire joining two fixed points $A$ and $B$ in a uniform magnetic field is:

$A$ wire carrying a current $I$ along the positive $x$-axis has length $L$. It is kept in a magnetic field $\overrightarrow{B} = (2\hat{i} + 3\hat{j} - 4\hat{k}) \text{ T}$. The magnitude of the magnetic force acting on the wire is $..........IL$.

Suppose an isolated north pole is kept at the centre of a circular loop carrying an electric current $i$. The magnetic field due to the north pole at a point on the periphery of the wire is $B$. The radius of the loop is $a$. The force on the wire is

$A$ conductor of length $l$ and mass $m$ is placed along the east-west line on a table. Suddenly,a certain amount of charge is passed through it and it is found to jump to a height $h$. The earth's magnetic induction is $B$. The charge passed through the conductor is:

Two long wires carrying currents $I_1$ and $I_2$ are arranged as shown in the figure. The wire carrying current $I_1$ is along the $x$-axis. The other wire carrying current $I_2$ is parallel to the $y$-axis,passing through the point $(0, 0, d)$. Find the magnetic force exerted on a segment of length $dl$ of the second wire at the point $O_2(0, 0, d)$ due to the wire carrying current $I_1$.