A current of 1 ampere flows about two loops of wire (loops A and B - the loops a

Question

A current of 1 ampere flows about two loops of wire (loops A and B - the loops are pictured together but are far apart and do not interact) in the counter clockwise direction. The large half circle is each loop, centered at point P marked by the black dot, has a radius of 10cm, while the small half circle in each loop )also centered at point P) has a radius of 5 cm. Calculate the magnetic field produced by the current at point P in both loops. What is the ratio: (field at point P in loop A/field at point P in loop B)?

Explanation / Answer

magnetic field due to first circuit         (o I / 4) [ (r2 -r1) / r1 r2 ] magnetic field due to second circuit       (o I /4) [ (r1 + r2) / r1 r2 ] Ratio of the field at point P is            = (o I / 4) [ (r2 -r1) / r1 r2 ] / (o I /4) [ (r1 + r2) / r1 r2 ]            = (r2-r1) / (r2 +r1)           = (10-5) / (10+ 5)           = (5/15)           = 1/3

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