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A long hairpin is formed by bending an infinitely long wire, as shown. If a current...

A long hairpin is formed by bending an infinitely long wire, as shown. If a current of 1.10 A is set up in the wire, what is the magnitude of the magnetic field at the point a? Assume R = 4.10 cm.

A long hairpin is formed by bending an infinitely

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Answer #1

the magneitc field due to stright wire is

B = μo I / 2πR

The magnetic field due to ciruclular loop is

B = μo I /2 R

for semi circle

B loop = B/2 =  μo I /4 R

The magnitude of the magnetic field at the point a is

B = ( μo I /4 R ) + ( μo I / 2πR ) =  (μoI / 4 R ) [ 1+ ( 2 / π )]

B = 4 pi * 10^-7 ( 1.10)/ 4 ( 0.0410) [ 1+ ( 2 / π )]

=13.79 * 10^-6 T

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