# Coaxial Cable

## Homework Statement

The diagram below depicts a cross section of coaxial conductor with an inner wire of diameter and an outer conducting sheath of inside diameter , and some material placed in the space between the two wires. Suppose that you have a coaxial wire with di= 2.85 mm, do= 6.25 mm and mylar ( k= 3.10) is placed in the space between the two wires. If there is a potential of 1 kV between the wires, how much energy is stored in a 10 m piece of cable?

## Homework Equations

$$U=\int V dQ$$

## The Attempt at a Solution

I perform the intergral and come up with a couple equations this one seem the best:
$$U= .5QV$$ Right?

#### Attachments

• InsulatedCoaxialCable.gif
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learningphysics
Homework Helper
How did you get 0.5QV ?

The way I'd do it is to find the charge per unit length on the inner wire... the charge per unit length on the outer conductor is just - the inner charge per unit length...

You can get this using Gauss' law... and the voltage = -integral E.dr

When you find the charge per unit length x... then the total charge is 10*x. The energy stored is 10*x*V.

You need to know the charge right? Or how charge varies with voltage or something?

The coax cable has capacitance per meter. You can look the equations up on wiki. Once you find the total capacitance (multiply by length), use E=(CV^2)/2.

Sterling

How did you get 0.5QV ?

The way I'd do it is to find the charge per unit length on the inner wire... the charge per unit length on the outer conductor is just - the inner charge per unit length...

You can get this using Gauss' law... and the voltage = -integral E.dr

When you find the charge per unit length x... then the total charge is 10*x. The energy stored is 10*x*V.

I do not know what I am doing wrong. Here is my work:
q/(кε) = EA, A = 2*pi*rx
E = q/(кεA) = q/(2кε*pi*rx)
V = -integral of Edr from a to b = -(q*ln(b/a))/(2кε*pi*x) = 1000 V
1000(2кε*pi)/ln(b/a) = q/x
(q/x)*10*1000 does not give me the answer. Where did I go wrong?

Thanks. It turns out my work is right, but the formula for energy is .5qV (i.e. C = q/V, so .5CV^2 = .5qV) , not qV.