Question

A long hairpin is formed by bending a very long wire, as shown. If the wire caries a current of 9 A, what is the magnitude and direction of the magnetic field at the point a? Take R = 10 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.

Tries 0/99

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.

Answer 1

a) Radius of the semicircular wire R = 10mm = 10^-2 m

current in the wire = 9 A

Magnetic fiel B at a,

= + (B₁ = Magnetic filed due to straight section of wire, B₂= Magnetic field due arc)

In magnitude

B_a = 2B₁ + B₂

Also B₁ = (.i) / (4R) (Magnetic file due to semi infinite wire)

B₂ = (.i) / (4R) (Magnetic field due to semicircular arc)

  

  

B_a = 4.6 x 10^-4 T

Direction of B_a is coming out of page, since current is anticlock wise.

= 4.6 x 10^-4 T

b) Distance between a and b is much larger than R,

Thus Magnetic field at b B_b , is contribution due to two parallel infinite wire

  

= 3.6 x 10^-4 T

Direction B_b is coming out of page

= 3.6 x 10^-4 T