Q. 66

Expert-verified
Found in: Page 740

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# 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 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