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Magnetic field due to current element

Question

Two circular coils made of similar wires but of radii 20 cm and 40 cm are connected in parallel. Find the ratio of the magnetic fields at their centers.

Moderate
Solution

When the coils are connected in parallel, the ratio of currents flowing in these coils will be equal to reciprocal of the ratio of their resistances

  i1i2=R2R1=ρl2/Aρl1/A (as both the coils are made of similar wires)   21=2πr22πr1=r2r1    B1B2=μ0i1/2r1μ0i2/2r2   B1B2=i1i2×r2r1  i1i2=r2r1   B1B2=r22r12=40202=41=4

 



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Two infinitely long straight parallel wires carry equal currents ‘i’ in the same direction and are 2 m apart. Magnetic induction at a point which is at same normal distance 2 m from each wire has magnitude 


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