The figure shows a cross section of a long conductor of a type called a coaxial

Question

The figure shows a cross section of a long conductor of a type called a coaxial cable and gives its radii (a,b,c) = (2.0, 1.8, 0.4 cm). Equal but opposite currents i = 90 A are uniformly distributed in the two conductors. The current in the inner cylinder is into the page, while the current in the outer is out of the page. Evaluate the magnitude of B(x) for the values asked below.

B(0.0 cm)?

B(0.2 cm)?

B(0.4 cm)?

B(1.0 cm)?

B(1.9 cm)?

B(2.0 cm)?

B(4.0 cm)?

The figure shows a cross section of a long conductor of a type called a coaxial cable and gives its radii (a,b,c) = (2.0, 1.8, 0.4 cm). Equal but opposite currents i = 90 A are uniformly distributed in the two conductors. The current in the inner cylinder is into the page, while the current in the outer is out of the page. Evaluate the magnitude of B(x) for the values asked below.

Explanation / Answer

1) B(0.0cm) = 0 (since there is I_enclosed)

2) B(0.2cm) = mue*I_enclosed/(2*pi*r)

I_enlcoed = 90*pi*0.2^2/pi*2^2 = 0.9 A

B(0.2cm) = 4*pi*10^-7*0.9/(2*pi*0.002) = 9*10^-5 T (

3)

B(0.4cm) = mue*I_enclosed/(2*pi*r)

I_enlcoed = 90*pi*0.4^2/pi*2^2 = 3.6 A

B(0.2cm) = 4*pi*10^-7*3.6/(2*pi*0.004) = 18*10^-5 T


4)
B(1cm) = mue*I_enclosed/(2*pi*r)

I_enlcoed = 90 A

B(0.2cm) = 4*pi*10^-7*90/(2*pi*0.001) = 1.8*10^-3 T

5)
B(1.9cm) = mue*I_enclosed/(2*pi*r)

I_enlcoed = 90A - 90*pi*(1.9^2-1.8^2)/pi*(2^2-1.8^2) = 46.18 A

B(1.9cm) = 4*pi*10^-7*46.18/(2*pi*0.019) = 4.861*10^-4 T

6)

B(2cm) = mue*I_enclosed/(2*pi*r)

I_enlcoed = 90-90 = 0A

B(2cm) = 0

7)

B(4cm) = mue*I_enclosed/(2*pi*r)

I_enlcoed = 90-90 = 0A

B(4cm) = 0

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