Speed of Current in a coaxial cable

[Kyuubi]

Homework Statement:

Calculate the inductance and capacitance per unit length of a long coaxial cable, and show that the current, or equivalently charge, wave has speed v =1/√(µ0ϵ0) = c which is the speed of light.

Relevant Equations:

Maxwell's equation in a vacuum.
Excuse me for not writing them, I'm not familiar with latex and I think I'll only need a conceptual answer. They should be in the photo though.

I've found the inductance and capacitance per unit length in a long coaxial cable. I even clearly see that if I multiply the two, I can get the speed of light. How do I begin to find the current wave and its speed though?

 

[haruspex]

Could you figure out the wave speed in a string of given tension and density? Maybe you could then use the same approach to model a wave in coax and find analogous equations using capacitance and inductance.