Two long straight parallel conductors $A$ and $B$ carrying currents $4.5 \ A$ and $8 \ A$ respectively are separated by $25 \ cm$ in air. The resultant magnetic field at a point $P$ which is at a distance of $15 \ cm$ from conductor $A$ and $10 \ cm$ from conductor $B$ is:

In the current-carrying conductor $(AOCDEFG)$ as shown,the magnetic induction at the point $O$ is ($R_1$ and $R_2$ are radii of arcs $CD$ and $EF$ respectively,$I$ = current in the loop,$\mu_0$ = permeability of free space).

$A$ straight wire of length $20 \text{ cm}$ carrying a current of $\frac{3}{\pi^2} \text{ A}$ is bent in the form of a circle. The magnetic field at the centre of the circle is

Two concentric circular loops,one of radius $R$ and the other of radius $2R$,lie in the $xy$-plane with the origin as their common center,as shown in the figure. The smaller loop carries current $I_1$ in the anti-clockwise direction and the larger loop carries current $I_2$ in the clockwise direction,with $I_2 > 2I_1$. $\vec{B}(x, y)$ denotes the magnetic field at a point $(x, y)$ in the $xy$-plane. Which of the following statement$(s)$ is(are) correct?
$(A)$ $\vec{B}(x, y)$ is perpendicular to the $xy$-plane at any point in the plane.
$(B)$ $|\vec{B}(x, y)|$ depends on $x$ and $y$ only through the radial distance $r = \sqrt{x^2 + y^2}$.
$(C)$ $|\vec{B}(x, y)|$ is non-zero at all points for $r$.
$(D)$ $\vec{B}(x, y)$ points normally outward from the $xy$-plane for all the points between the two loops.

$A$ current $I$ flows in a circular arc of radius $r$ subtending an angle $\theta$ at the centre $O$ as shown in the figure. Find the magnetic field at the centre $O$ of the circle.

The magnetic field at the center of a circular coil carrying current '$I$' for a single turn of a given length of wire is '$B$'. The same wire is bent into a circular coil having two turns. When the same current '$I$' passes through it, the value of the magnetic field becomes: