Two concentric coplanar circular loops of radii $$r1$$ and $$r2$$ carry currents $$i1$$ and $$i2$$, respectively, in opposite directions (one$$ clockwise and the other anticlockwise.$$) The magnetic induction at the centre of the loops is half of that due to $$i1$$ alone at the centre. If $$r2$$ $$=$$ $$2r1$$ , the value of $$i2/i1$$ is

Question

Infinity Learn · Accepted Answer

Magnetic field at the centre due to smaller $$loopB1$$ $$=$$  μ$$04$$π .  $$2$$$$π$$$$i1r1$$                 ….$$(i)Due$$ to bigger loop, $$B2$$ $$=$$  μ$$04$$π .  $$2$$$$π$$$$i2r2So$$, net magnetic field at $$centreB=B1$$−$$B2$$ $$=$$  μ$$04$$π × $$2$$π  $$i1r1$$ − $$i2r2According$$ to question, $$B=12$$  ×  $$B1$$⇒μ$$04$$π . $$2$$π  $$i1r1$$ − $$i2r2$$ $$=12$$  ×  μ$$04$$π . $$2$$$$π$$$$i1r1i1r1$$ − $$i2r2$$ $$=$$ $$i12r1$$ ⇒ $$i2r2$$ ⇒ $$i12r1$$ ⇒$$i1i2$$ $$=1$$    $$r2$$ $$=2r1$$

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Two concentric coplanar circular loops of radii r1 and r2 carry currents i1 and i2, respectively, in opposite directions (one clockwise and the other anticlockwise.) The magnetic induction at the centre of the loops is half of that due to i1 alone at the centre. If r2 = 2r1 , the value of i2/i1 is

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