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(D) The magnetic field at the centre of a loop is zero if the current splits into two paths such that the magnetic fields produced by the two paths at

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$P$ and $R$

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(D) The magnetic field at the centre of a loop is zero if the current splits into two paths such that the magnetic fields produced by the two paths at the centre are equal in magnitude and opposite in direction.In configuration $P$,the two paths consist of one thick and one thin wire each. Since the total resistance of each path is the same,the current divides equally. The magnetic fields produced by these two symmetric paths cancel each other out.In configuration $R$,the two paths are also symmetric,each consisting of one thick and one thin wire connected in series. Thus,the current divides equally,and the magnetic field at the centre is zero.In configuration $Q$,the two paths consist of two thick wires and two thin wires respectively. Since the resistances are different,the currents are unequal,and the magnetic fields do not cancel out.Therefore,the magnetic field at the centre is zero in cases $P$ and $R$.

Two thick wires and two thin wires,all of the same material and same length,form a square in three different ways $P, Q,$ and $R$ as shown in the figure. With the correct connections shown,the magnetic field due to the current flow at the centre of the loop will be zero in the case of:

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