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Q. 86

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

86. III High-frequency signals are often transmitted along a coaxial CALC cable, such as the one shown in FIGURE CP30.86. For example, the cable TV hookup coming into your home is a coaxial cable. The signal is carried on a wire of radius while the outer conductor of radius is grounded. A soft, flexible insulating material fills the space between them, and an insulating plastic coating goes around the outside.

a. Find an expression for the inductance per meter of a coaxial cable. To do so, consider the flux through a rectangle of length that spans the gap between the inner and outer conductors.

b. Evaluate the inductance per meter of a cable having and .

Part (a) The self-inductance per unit length of the cable is henries/m

Part (b) The inductance per meter is

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Step by Step Solution

Part (a)

Radio frequency AC are transmitted by means of cables over a large distance. A cable consists of two coaxial cylindrical conductors of radii and . The currents in the conductors are equal in magnitude but opposite in directions. Thus, there is no magnetic field outside these conductors. Thus, the cable is non-radiating. There will, however, be a magnetic flux between the two cylinders.

Let there be a current of I A through the conductors

The magnetic field B is at distance r from the axis and within the region between the two cylinders.

Here, the flux through the area between r and r+dr, and of unit length, is given by

Thus, total flux between the unit length of the cable is given by

Thus, self-inductance per unit length of the cable is henries/m

Part (b)

Part(b)

Here, , and

Thus, from the result of (a) above, the inductance per meter is

The inductance per meter is

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