In the given figure calculate magnetic field induction at the point $P$ and $M$.

A rectangular conducting loop of length $4\sqrt{2}m$ and breadth $4m$ carrying a current of $5A$ in the anti-clockwise direction is placed in the $xy$ -plane. The magnitude of the magnetic induction field vector $B$ at the intersection of the diagonal is $\left(\mathrm{u}\mathrm{s}\mathrm{e}\mathrm{ }{\mu }_0=4\pi \times {10}^{-7}N{A}^{-2}\right)$

Two long straight parallel wires, carrying (adjustable) currents $I_1$ and $I_2$ , are kept at a distance $d$ apart. If the force $F$ between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other, the graph showing the dependence of $F$, on the product $I_1{I}_2$ , would be:

An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current $I$ along the same direction is shown in Figure. Magnitude of force per unit length on the middle wire $B$ is given by

A rigid square loop of side $\mathrm{‘}\mathrm{a}’$ and carrying current ${\mathrm{I}}_2$ is lying on a horizontal surface near a long current ${\mathrm{I}}_1$ carrying wire in the same plane as shown in figure. The net force on the loop due to the wire will be:

A wire carrying current $\text{I}$ has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to $\text{X}$ -axis while semicircular portion of radius $\text{R}$ is lying in $\text{Y}$ -$\text{Z}$ plane. Magnetic field at point $\text{O}$ is :

Consider two straight parallel conductors $A$ and $B$ separated by a distance $x$ and carrying individual currents $i_A \mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }{i}_B$ respectively. If the two conductors attract each other, it indicates that

As shown in the figure, two infinitely long, identical wires are bent by ${90}^o$ and placed in such a way that the segments $LP$ and $QM$ are along the $x$ - axis, while segments $PS$ and $QN$ are parallel to the $y$ - axis. If $OP=OQ=4cm,$ and the magnitude of the magnetic field at $O$ is ${10}^{-4} T,$ and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at $O$ will be $\left({\mu }_0=4\pi \times {10}^{-7}N{A}^{-2}\right):$

An arrangements with a pair of quarter circular coils of radii $r$ and $R$ with a common centre $C$ and carrying a current $I$ is shown.

The permeability of free space is ${\mu }_0$. The magnetic field at $C$ is

Two very long, straight, and insulated wires are kept at $90°$ angle from each other in $\mathrm{x}\mathrm{y}$ plane as shown in the figure.

These wires carry currents of equal magnitude $I$ , whose direction are shown in the figure. The net magnetic field at point $P$ will be: