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(D) The magnetic field at the centre of the square is zero if the currents in the opposite segments produce equal and opposite magnetic fields at the

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$P$ and $R$ only

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(D) The magnetic field at the centre of the square is zero if the currents in the opposite segments produce equal and opposite magnetic fields at the centre.In case $P$,the two paths are symmetric and consist of one thick and one thin wire each. Thus,the resistance of both paths is equal,leading to equal currents. The magnetic fields produced by these currents cancel each other out at the centre.In case $Q$,the paths are asymmetric (one path has two thick wires,the other has two thin wires). The resistances are unequal,so the currents are unequal,and the magnetic fields do not cancel out.In case $R$,the two paths are again symmetric,each consisting of one thick and one thin wire. Thus,the currents are equal,and the magnetic fields at the centre 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 current connection indicated. The magnetic field at the centre of the square is zero in cases:

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