a coaxial cable consists of an inner wire radius 2mm and an outer metal cylinder

Question

a coaxial cable consists of an inner wire radius 2mm and an outer metal cylinder of inner radius 5mm and outer radius 9mm. the inner wire has a current of 7A and out of hte page and the outer cylinder has a current of 10A into the page.

8) A coaxial cable consists of an inner wire radius 2mm and an outer metal cylinder of inner radius 5mm and outer radius of 9mm. The Inner wire has a current of 7 A out of the page and the outer cylinder has a current of 10 A into the page. a) What is the magnetic field magnitude and direction at a distance of 2.3mm from the center? b) What is the magnetic field magnitude and direction at a distance of 7mm from the center? c) 10mm from the center?

Explanation / Answer

At 2.3 mm from the center, it encloses the whole inner wire. thus, by Ampere's law and symmetry,

B = uo Ienc / (2 pi r)

= 6.09*10^-4 T, counterclockwise   [ANSWER, PART A]

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At 7 mm from the center, it encloses also some of the oiter wire. Thus, by some geometry,

Ienc = 7 A - 4.2857 A = 2.714 A, out of the page.

Thus,

B = 7.75*10^-5 T, counterclockwise   [ANSWER, PART B]

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10 m from the center, you enclose both wires,

Ienc = 3 A, into the page. Thus,

B = 6.00*10^-5, clockwise   [ANSWER, PART C]

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