1. A long hairpin is formed by bending a very long wire, as shown. If the wire c
ID: 1461623 • Letter: 1
Question
1. A long hairpin is formed by bending a very long wire, as shown. If the wire caries a current of 15 A, what is the magnitude and direction of the magnetic field at the point a? Take R = 11 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.
2. 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
The formula for magnetic field due to semi straight wire
B = uo i/ 4 pi R
magnetic field at the center of the circular arc is
B = uo i/ 4R
the magnitude of magnetic field at point a is
B = 2 ( uo i/ 4 pi R+ uo i/ 4R)
= uo i/ 2R ( 1/ pi + 1/2)
= 4 pi * 10 ^-7 ( 15)/ 2 ( 11 * 10 ^-3 m) ( 1/pi + 1/2)
=0.7 mT
the magnitude of magnetic field at point b is
B = 2 uo i/ 2 pi R
= 4 pi * 10 ^-7 ( 15)/ pi ( 11 * 10 ^-3 m)
=0.545 mT
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