The resistance of the three parts of a circular loop is . . .

Question : The resistance of the three parts of a circular loop is shown in the figure. The magnetic field at the centre O is 

a) Zero

b) 2µ₀i/5r

c) µ₀i/6r

d) µ₀i/3r

Doubt by Mohini

Solution : 

If you closely look at the figure then you will realise that current is entering the circular loop through 'a' and leaving the loop through the points 'b' and 'c'.

R_ab=R_ac = R

Both the parts 'ab' and 'ac' are having the resistance R as well as same current I. So the potential drop across each of them will be zero.

Both the parts are initially starts at the same point 'a' and have the same potential drop so we can say that the potential at point 'b' and 'c' will be same and hence we can conclude that no current will flow through 'bc'.

Now, Magnetic field due to the current in wire 'ab' will be given by 

Both the magnetic field are equal in magnitude but opposite in direction, so they will cancel out each other. So the net magnetic field at the centre O will be zero.

Hence, a) would be the correct option.