The strength of the magnetic field at a point $r$ near a long straight current-carrying wire is $B$. The field at a distance $\frac{r}{2}$ will be

Two concentric coils $X$ and $Y$ of radii $16 \, cm$ and $10 \, cm$ lie in the same vertical plane containing $N-S$ direction. Coil $X$ has $20$ turns and carries $16 \, A$. Coil $Y$ has $25$ turns and carries $18 \, A$. Coil $X$ has current in anticlockwise direction and coil $Y$ has current in clockwise direction for an observer looking at the coils facing the west. The magnitude of the net magnetic field at their common centre is:

$A$ current flows through a circular coil of radius $R$. Find the distance from the center on the axis where the magnetic field is $\frac{1}{8}$th of the magnetic field at the center.

Equal current $i$ is flowing in three infinitely long wires along positive $x, y$ and $z$ directions. The magnetic field at a point $(0, 0, -a)$ would be:

Assertion: In electric circuits,wires carrying currents in opposite directions are often twisted together.
Reason: If the wires are not twisted together,the combination of the wires forms a current loop,and the magnetic field generated by the loop might affect adjacent circuits or components.

$A$ long straight wire carrying a current of $30 \ A$ is placed in an external uniform magnetic field of induction $4 \times 10^{-4} \ T$. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point $2.0 \ cm$ away from the wire is $(\mu_0 = 4 \pi \times 10^{-7} \ H/m)$.