3. Coaxial cables are often used to connect electrical devices, for instance in receiving signals in TV cable systems. Figure below shows a long coaxial cable as consisting of two thin concentric cylindrical conducting shells of radii a and b and length 1. The conducting shells (regions: r < a and a < r < b are hollow) carry the same current I in opposite directions. Imagine that the inner conductor carries current to a device and that the outer one acts as a return path carrying the current back to the source. The magnetic field is perpendicular to the blue rectangle of length I and width b-a; the cross section of interest is shown.

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3. Coaxial cables are often used to connect electrical devices, for instance in receiving
signals in TV cable systems. Figure below shows a long coaxial cable as consisting of
two thin concentric cylindrical conducting shells of radii a and b and length 1. The
conducting shells (regions: r < a and a < r < b are hollow) carry the same current I
in opposite directions. Imagine that the inner conductor carries current to a device and
that the outer one acts as a return path carrying the current back to the source. The
magnetic field is perpendicular to the blue rectangle of length / and width b-a; the cross
section of interest is shown.
b
dr
B
Calculate the self-inductance L of this cable.
Calculate the total energy stored in the magnetic field of the cable.
Transcribed Image Text:3. Coaxial cables are often used to connect electrical devices, for instance in receiving signals in TV cable systems. Figure below shows a long coaxial cable as consisting of two thin concentric cylindrical conducting shells of radii a and b and length 1. The conducting shells (regions: r < a and a < r < b are hollow) carry the same current I in opposite directions. Imagine that the inner conductor carries current to a device and that the outer one acts as a return path carrying the current back to the source. The magnetic field is perpendicular to the blue rectangle of length / and width b-a; the cross section of interest is shown. b dr B Calculate the self-inductance L of this cable. Calculate the total energy stored in the magnetic field of the cable.
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