$A$ uniform wire is bent in the form of a circle of radius $R$. $A$ current $I$ enters at $A$ and leaves at $C$ as shown in the figure. If the length $ABC$ is half of the length $ADC$,the magnetic field at the centre $O$ will be

Two circular loops $L_1$ and $L_2$ of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop $L_1$ is $R_1$ and that of $L_2$ is $R_2$. The distance between the centres of the loops is $\sqrt{3} R_1$. The magnetic field at the centre of $L_2$ shall be zero if

At what distance from a long straight wire carrying a current of $12 \, A$ will the magnetic field be equal to $3 \times 10^{-5} \, Wb/m^2$?

Two long parallel wires carrying currents $I_1 = 4 \ A$ and $I_2 = 3 \ A$ in opposite directions are placed at a distance of $d = 5 \ cm$ from each other. $A$ point $P$ is at equidistance from both the wires such that the lines joining the point $P$ to the wires are perpendicular to each other. The magnitude of the magnetic field at point $P$ is ( $\mu_0 = 4 \pi \times 10^{-7} \ T \cdot m/A$ ).

Which of the following graphs represents the variation of magnetic field $B$ with perpendicular distance $r$ from an infinitely long,straight conductor carrying current?

Magnetic field due to a ring having $n$ turns at a distance $x$ on its axis is proportional to (if $r$ = radius of ring)