$A$ long straight wire carries a current of $18 \,A$. The magnitude of the magnetic field at a point $12 \,cm$ from it is

Two concentric circular coils $X$ and $Y$ of radii $16\; cm$ and $10\; cm$ respectively,lie in the same vertical plane containing the north to south direction. Coil $X$ has $20$ turns and carries a current of $16\; A$. Coil $Y$ has $25$ turns and carries a current of $18\; A$. The sense of the current in $X$ is anticlockwise,and clockwise in $Y$,for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.

$A$ current $i$ is flowing in a straight conductor of length $L.$ The magnetic induction at a point on its axis at a distance $\frac{L}{4}$ from its centre will be

$A$ circular coil carrying current $I$ has a radius $r$ and $n$ turns. The magnetic field along the axis of a coil at a distance $x = 2\sqrt{2}r$ from its centre is (where $\mu_0$ is the permeability of free space).

$A$ wire in the form of a circular loop of one turn carrying a current produces a magnetic field $B$ at the centre. If the same wire is looped into a coil of two turns and carries the same current,the new value of magnetic induction at the centre is

Magnetic field $dB$ due to a current element at any point on its axis is . . . . . . .