Question

Current I flows along the positive z-direction in the inner conductor of a long coaxial cable and returns through the outer conductor. The inner conductor has radius a, and the inner and outer radii of the outer conductor are b and c, respectively. (a) Determine the magnetic field in each of the following regions: 0 ≤ r ≤ a, a ≤ r ≤ b, b ≤ r ≤ c, and r ≥ c. (b) Plot the magnitude of H as a function of r over the range from r = 0 to r = 10 cm, given that I = 10 A, a = 2 cm, b = 4 cm, and c = 5 c

Answer 1

A) determine magnetic fields

For 0 ≤ r ≤ a

Magnetic field = ∅
`(rI)/(2\pi a^2)`

For a ≤ r ≤ b

Magnetic field = ∅
`(I)/(2\pi r)`

For b ≤ r ≤ c

Magnetic field in the region = ∅
`(I)/(2\pi r) [ c^2 - r^2 / c^2-b^2 ]`

For r ≥ c

magnetic filed in the region = 0

B ) attached below

Step-by-step explanation:

A) Determine the magnetic field in the following regions

i) For 0 ≤ r ≤ a

Magnetic field = ∅
`(rI)/(2\pi a^2)`

attached below is the detailed solution

ii) For a ≤ r ≤ b

Magnetic field = ∅
`(I)/(2\pi r)`

attached below is the detailed solution

iii) For b ≤ r ≤ c

Magnetic field in the region = ∅
`(I)/(2\pi r) [ c^2 - r^2 / c^2-b^2 ]`

attached below is the detailed solution

iv) For r ≥ c

magnetic filed in the region = 0 and this is because the net current enclosed in the region = 0