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# A coaxial cable consists of a wire of radius 'a' surrounded by a concentric conducting sleeve of inner radius 'b' and outer radius 'c'.

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A coaxial cable consists of a wire of radius 'a' surrounded by a concentric conducting sleeve of inner radius 'b' and outer radius 'c'.

A current flows in the wire of radius 'a' out of the page; this current is spread uniformly over the cross section of the wire. An equal current flows in the opposite direction in the sleeve; this current is spread uniformily over the cross section of the sleeve.

1) find the magnetic field in the space between the wire and the sleeve; and also in the space outside the sleeve. (that is , find the mag field at a distance 'r' from the center of the wire when b<r<c and when r>c )

2)why is coax cable used in some applications? What are the physical characteristics that make its use desirable in some situations? (the answer to this part of the question may make use of the results for part ).

https://brainmass.com/physics/amperes-law/10626

#### Solution Preview

1.)
<br>when b<r<c:
<br>let current in wire and the sleeve is i.
<br>because, current density in the sleeve = i/(pi*(c^2 - b^2))
<br>hence, the curren of the sleeve within the loop of radius r:
<br>i(r) = i*pi*(r^2 - b^2)/(pi*(c^2 - b^2))
<br>=> i(r) =i*(r^2 - b^2)/*(c^2 - b^2)
<br>
<br>Now, by Ampere's circuital law ...

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