(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A coaxial transmission line consists of an inner cylindrical conductor of radius a = 1 mm and a

cylindrical outer conductor chosen to make the characteristic impedance 75 ohm. The space

between the conductors is lled with a gas which can stand a maximum eld of 105 V/m

without dielectric breakdown. Estimate the maximum mean radio-frequency power that

can be transmitted along this line into a matching load.

2. Relevant equations

On transmission line

## Z = \sqrt{L/C} ##

For coaxial with radius a and b:

##C = \frac{2\pi \epsilon \epsilon_0}{ln(b/a)} ##

##L = \frac{\mu_0 ln(b/a)}{2\pi} ##

3. The attempt at a solution

The voltage between the two conductors is by Gauss's law:

## V = \int \boldsymbol{E} \cdot d\boldsymbol{r} = E_0 ln(b/a) ##

hence:

## V_{max} = E_{max} ln(b/a) ##

also:

##Z = \sqrt{\mu / \epsilon \epsilon_0} \frac{ln(b/a)}{2\pi} ##

Using ##P = VI = V^2/Z ## and asuuming ##epsilon \approx 1## gives:

##P_{max} = 0.21 GW##, but the answer is supposed to be 104 W.

What am I doing wrong? Many thanks!

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# Homework Help: Power Transmitted in a Coaxial Cable

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