Question

Chapter 29, Problem 020 In the figure, part of a long insulated wire carrying current i = 2.10 mA is bent into a circular section of radius R = 5.97 cm. What are (a) the x-component, (b) the y-component, and (c) the z-component of the magnetic field at the center of curvature C if the circular section lies in the plane of the page as shown? What are (d) the x-component, (e) the y-component, and (f) the z-component of the magnetic field at the center of curvature C if the circular section is perpendicular to the plane of the page after being rotated 90° counterclockwise as indicated? Units Units Units (a) Number (b) Number (c) Number (d) Number (e) Number (f) Number Units Units Units

Answer 1

The system can be taken as two independent shapes of one coil and one straight wire.

The magnetic field due to the current is in the -z direction. (Right hand thumb rule)

Β = μοΙ /2πι-

When the coli is in plane with the wire, the magnetic field due to the coil will be in the +z directiin and is given by

Β = μο1/2r

So, the total magnetic field is

Here, I = 2.1 mA

r = 5.97 cm = 0.0597 m

Due to wire = 4*3.14*10^-7*2.1*10^-3/(2*3.14*0.0597) = 7.04 nT (nano tesla)

Due to coil = 4*3.14*10^-7*2.1*10^-3/(2*0.0597) = 0.221 nT.

So, total magnetic field = 0.221-7.04 = -6.819 nT

The first 3 answers are

1) 0 T

2) 0 T

3) -6.819*10^-9 T

When the coli is rotated 90 degrees,

The field due to the coil is in the +x direction.

So, answer for 4 is

4) 0.221*10^-9 T

5) 0 T (remains unchanged)

The field due to the wire remains in the - z direction.

6) -7.04*10^-9 T