Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

(8c29p11) A long hairpin is formed by bending a very long wire, as shown. If the

ID: 1781452 • Letter: #

Question

(8c29p11) A long hairpin is formed by bending a very long wire, as shown. If the wire caries a current of 12 A, what is the magnitude and direction of the magnetic field at the point a? Take R = 7 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

i = 12 A, R = 7 * 10-3 m

magnitude of the magnetic field at point a = [2 mu0 i / 4 pi R] + [mu0 i / 4 R]

B = [mu0 i / 2 R] [1/pi + 1/2]

= [4 pi * 10-7 * 12 / 2 * 7 * 10-3] [1/pi + 1/2]

= 8.8 * 10-4 T = 0.88 mT

magnitude of the magnetic field at point b = 2 [mu0 i / 2 pi R]

= 2 [4 pi * 10-7 * 12 / 2 pi * 7 * 10-3]

= 6.86 * 10-4 T = 0.686 mT