Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre,find the ratio of the magnetic field due to one coil and the resultant magnetic field by both coils,if the same current is flowing through them.

The magnetic field due to a straight conductor of uniform cross section of radius $a$ and carrying a steady current is represented by

Two straight horizontal parallel wires are carrying the same current in the same direction, and $d$ is the distance between the wires. You are provided with a small freely suspended magnetic needle. At which of the following positions will the orientation of the needle be independent of the magnitude of the current in the wires?

$A$ square frame of side $1 \ m$ carrying a current $I$ produces a magnetic field $B$ at its centre. The same current is passed through a circular coil having the same perimeter as the square. The magnetic field at the centre of the circular coil is $B^{\prime}$. The ratio of $\frac{B}{B^{\prime}}$ is

The figure shows the cross-section of a long cylindrical conductor through which an axial hole of radius $r$ is drilled with its centre at point $A$. $O$ is the centre of the conductor. If an identical hole were to be drilled centred at point $B$ while maintaining the same current density,the magnitude of the magnetic field at $O$:

$A$ horizontal overhead power line is at a height of $4\,m$ from the ground and carries a current of $100\,A$ from east to west. The magnetic field directly below it on the ground is $(\mu _0 = 4\pi \times 10^{-7}\,TmA^{-1})$