Figure shows a square loop ABCD with edge length a. The resistance of the wire ABC is r and that of ADC is 2r. Find the magnetic field B at the centre of the loop assuming uniform wires.

Question

Philoid · Accepted Answer

Resistance of wire ADC is given twice that of wire ABC. hence current flow through ADC is half of ABC

i.e.,

--------------------(1)

also ---------------(2)

Equating equations (1) and (2), we get

and

Hence, magnetic field at centre O due to wire AB and BC

and magnetic field at centre o due to wire AD and DC

Also , so

Hence net magnetic field at centre O