Question

(d) What are the x- and y-components of the magnetic field at point E located at (x,y) = (−1.0,1.0) cm as shown? (3pt)

A long, straight wire of radius a = 2.0 cm is located along the z-axis and carries a current I = 2.1 A in the negative z-direction. A cylindrical conducting shell of inner radius b= 4.0 cm and outer radius c = 5.7 cm coaxial with the wire carries a uniformly distributed current 12 = 7.1 A in the positive z-direction as shown. у Figure 1:

Answer 1

The radius at point E is

r= V12 + 12 = 12 cm

or r = 0.014 m

The current enclosed inside a cylinder of radius r is

i = Tij? = 2.1 2/2° = 1.05 A

The magnitude of magnetic field at E is

Β = μοι = 4πX 10-7x1.05 2 = 1.485 x 10-5T 2π x 0.014

The magnetic field is clockwise

The x component of B is

B, = B cos(45') = 1.485 x 10-5 x cos(45°) = 1.05 x 10-5T = 10.5 4T

The y component is

B, = B sin(45°) = 1.485 x 10-5 x sin(45%) = 1.05 x 10-5T = 10.5uT