Q. 174.5( 2 Votes )

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.



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






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