A coaxial cable consists of a single wire surrounded by a cylindrical metallic braid as shown in Fig.
The inner wire carries current to the other end of the cable and the outer braid carries the return current and is generally considered ground. Describe the magnetic field in the space between conductors B (a < r < b) and outside cable B (r > b).
Text Solution
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Sol. We take a circular closed path in the space between conductors, to apply Ampere's law.
B2 π r = μ 0 I
B = 
The result is same as in case of a long wire. The current in the outer conductor has no bearing on it. In Ampere's law the current that lies within the closed curve is included. As long as the currents outside the closed curve do not affect the symmetry of the field; they do not contribute to the field along the curve at all
Similarly we can draw a circular closed, curve because from symmetry the expected field is circular. The net current enclosed in the closed curve is zero as there are two equal currents in opposite directions. Therefore Ampere's law becomes
B2 π r = 0
or B = 0
The field outside the cable is zero.
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