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Q. 66

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 740

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Short Answer

High-frequency signals are often transmitted along a coaxial cable, such as the one shown in FIGURE P26.66. 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 (i.e., at ). An insulating material fills the space between them, and an insulating plastic coating goes around the outside.

a. Find an expression for the capacitance per meter of a coaxial cable. Assume that the insulating material between the cylinders is air.

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

a. The expression for the capacitance per meter of a coaxial cable is

b. The capacitance of a cable is

See the step by step solution

Step by Step Solution

Step 1: Given Information (Part a)

The signal is carried on a wire of radius

Voltage

Step 2: Explanation (Part a)

a. Applying Gauss's law for the cylinder with linear charge density , to get electric field outside of a cylinder as

Potential difference for two cylinders will be

Find the capacitance per unit length as

Hence, the expression for the capacitance per meter of a coaxial cable is

Step 4: Given Information (Part a)

The signal is carried on a wire of radius and

Step 5: Explanation (Part b)

In the given numerical case, we will have

Substitute the values,

Multiply the expression,

Hence, the capacitance of a cable is

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