Question

given a coaxial cable of length 30 centimeter with inner radius 1 millimeter and 4 millimeter respectively, the space between the conductors is assumed to be filled with air. the total charge on the inner conductor is 1 nano coulomb. find the charge density on each charge and also the internal field

Answer 1

Answer on Question #72376-Physics-Electromagnetism

Given a coaxial cable of length 30 centimeter with inner radius 1 millimeter and 4 millimeter respectively, the space between the conductors is assumed to be filled with air. The total charge on the inner conductor is 1 nano coulomb. Find the charge density on each charge and also the internal field

Solution

The charge density on inner radius is

$$\sigma = \frac {q}{2 \pi r _ {1} l} = \frac {1 \cdot 1 0 ^ {- 9}}{2 \pi (0 . 0 0 1) (0 . 3)} = 5 3 \frac {\mu C}{m ^ {2}}.$$

The charge density on outer radius is

$$\sigma = \frac {q}{2 \pi r _ {1} l} = \frac {1 \cdot 1 0 ^ {- 9}}{2 \pi (0 . 0 0 4) (0 . 3)} = 1 3 \frac {\mu C}{m ^ {2}}.$$

The internal field is

$$E = 0, \text{ if } 0 < r < 0.001 \, \text{m}.$$

If $0.001 < r < 0.004 \, \text{m}$

$$E = \frac {q}{2 \pi \epsilon_ {0} r l}$$ $$E = \frac {1 \cdot 1 0 ^ {- 9}}{2 \pi (8 . 8 5 \cdot 1 0 ^ {- 1 2}) (0 . 3)} \frac {1}{r} = \frac {6 0}{r} \frac {V}{m}.$$

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