As shown in the figure, a current i = 12 A is set up in a long hairpin conductor

Question

As shown in the figure, a current i = 12 A is set up in a long hairpin conductor formed by bending a wire into a semicircle of radius R = 13 mm. Point b is midway between the straight sections and so distant from the semicircle that each straight section can be approximated as being an infinite wire. What is the magnitude and direction (take the sign of B to be positive if the direction is out of the page, and negative if B is into the page.) of at point a? What is the magnitude and direction of at point b? The distance between a and b is much larger than R (each straight section is infinite).

Explanation / Answer

Bb = 2*I/2r =I/R =4*10-7*12/0.013 =3.692 x10-4 T

Ba = I/4R + 2*I/4R =4*10-7*12/4*0.013 + 2*10-7*12/0.013 =4.746 x10-4 T

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