Find the resultant magnetic field at the origin due to four infinitely long wires. Each wire produces a magnetic field of magnitude $B$ at the origin.

$A$ very long conducting wire is bent in a semicircular shape from $A$ to $B$ as shown in the figure. The magnetic field at point $P$ for the steady current configuration is given by:

An electric current is flowing through a circular coil of radius $R$. The ratio of the magnetic field at the centre of the coil and that at a distance $2\sqrt{2}R$ from the centre of the coil on its axis is:

$A$ circular loop is kept in the vertical plane that contains the north-south direction. It carries a current that is towards the south at the topmost point. Let $A$ be a point on the axis of the circle to the east of it and $B$ be a point on this axis to the west of it. The magnetic field due to the loop is:

In the following figure,a wire bent in the form of a regular polygon of $n$ sides is inscribed in a circle of radius $a$. The net magnetic field at the centre will be

Write the equation for the magnetic field due to a circular current-carrying loop at a point on the axis of the loop. Give its special cases.