Q17 of 92 Page 249

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.




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






More from this chapter

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Consider a 10 cm long piece of a wire which carries a current of 10A. Find the magnitude of the magnetic field due to the piece at a point which makes an equilateral triangle with the ends of the piece.

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A long, straight wire carries a current i. Let B1 be the magnetic field at a point P at a distance d from the wire. Consider a section of length ℓ of this wire such that the point P lies on the perpendicular bisector of the section. Let B2 be the magnetic field at this point due to this section only. Find the value of d/ℓ so that B2 differs from B1 by 1%.

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Figure shows a square loop of edge a made of a uniform wire. A current i enters the loop at the point A and leaves it at the point C. Find the magnetic field at the point P which is not the perpendicular bisector of AB at a distance a/4 from it.


 19

Consider the situation described in the previous problem. Suppose the current i enters the loop at the point A and leaves it at the point B. Find the magnetic field at the centre of the loop.