A steady current is set up in a cubic network composed of wires of equal resistance and length d as shown in Fig. What is the magnetic field at centre P due to the cubic network?

Explanation

By symmetry of the circuit, it is clear that for each current carrying wire there is another wire such that it cancels the field of the first. For e.g. the field at P due to wire AB is cancelled by field of wire GF. Field of wire CD is cancelled by wire HE. Similarly, AH and CF, DG and BE, BC and HG, AD and .EF fields are cancelled and therefore net field is zero at .P..