Figure shows a square loop made from a uniform
wire. Find the magnetic field at the centre of the square
if a battery is connected between the points A and C.

Explanation

The current will be equally divided at A. The fields at the centre due to the currents in the wires AB and DC will be equal in magnitude and opposite in direction . The resultant of these two fields will be zero .
Special case :
(i) If the wire is infinitely long then the magnetic field at 'P' (as shown in the figure) is given by (using `theta_(1)=theta_(2)=90^(@)` and the fromula of 'B' due to straight wire)
`B=(mu_(0)I)/(2pir)rArrBprop(I)/(r)`

The direction of `vecB` at various is as shown in the figure. The magnetic lines of force will be concentric circles around the wire (as shown earlier)
(ii) If the wire is infinitely long but 'P' is as shown in the figure . The direction of `vecB` at various points is as shown in the figure . At 'P'
`B=(mu_(0)I)/(4pir)`