A long hairpin is formed by bending a very long wire, as shown. If the wire cari

Question

A long hairpin is formed by bending a very long wire, as shown. If the wire caries a current of 8 A, what is the magnitude and direction of the magnetic field at the point a? Take R = 5 mm. Take the sign of B to be positive if the direction is out of the paper and negative if B is into the paper. You need to enter the number with its sign and a space and the unit.

What is the magnitude and direction of the magnetic field at the midpoint b? The distance between a and b are much larger than R (each straight section is "infinite"). Take the sign of B to be positive if the direction is out of the paper and negative if B is into the paper.

Explanation / Answer

magnetic field due to long wire = B1 = 2*uo*I/(4*pi*R)

B1 = (2*4*pi*10^-7*8)/(4*pi*0.005) = 0.00032 T

magnetic field due to semicirdular arc = B2 = uo*I/4R

B2 = (4*pi*10^-7*8)/(4*0.005) = 0.0005

B = B1 + B2 = 0.00082 T

++++++++++

magnetic field due to long wire = B1 = 2*uo*I/(pi*R)

B1 = (2*4*pi*10^-7*8)/(2*pi*0.005) = 0.00064 T

as a the distance ob b is very large

magnetic field due to semicirdular arc = B2 = 0

B = B1 + B2 = 0.00064 T

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