The resistances of three parts of a circular loop are as shown in the figure. The magnetic field at the centre $O$ is :-
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There will be no current through the branch $B C$. and $\quad i_{A B}=i_{A C}$
and net magnetic field due to $A B \& A C=0$. Because $A B$ produces magnetic field inwards $\& A C$ produces magnetic field outwards at $O .$
Net magnetic field is zero.
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