Figure shows a square loop made from a uniform wire. If a battery . . .

Question : Figure shows a square loop made from a uniform wire. If a battery is connected between the points A and C, what will be the magnetic field at the centre of the square? 

Dout by Tanisha

Solution : 
Current through the branch ADC will be equal to the current through the branch ABC because both the branches have equal length and hence equal resistance. So the current through each of them will be I/2.

Now, the magnitude of the magnetic field produced by each side of the square at the centre will be same, let us take it B but the direction of magnetic field will be different, which is given by Right Handed Thumb Rule.

B_AB = B (Outside)
B_BC = B (Outside)

B_CD = B (Inside)

B_DA = B (Inside)

Hence, net magnetic field at the centre will be 

B_NET = B_AB+B_BC+B_CD+B_DA
B_NET = B+B+(-B)+(-B)
B_NET = 0