1. The problem statement, all variables and given/known data 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? 2. Relevant equations [tex] U=\int V dQ[/tex] 3. The attempt at a solution I perform the intergral and come up with a couple equations this one seem the best: [tex] U= .5QV[/tex] Right?
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.
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
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?
This page has the equation for the capacitance.. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capcyl.html C/L=2*pi*k*ε_{0}/ln(do/di) So C= L*2*pi*k*ε_{0}/ln(do/di) Then Energy is U = 0.5*C*V^{2} Note it's V squared not V.
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.