Speed of Current in a coaxial cable

AI Thread Summary
The discussion focuses on calculating the speed of current in a coaxial cable using its inductance and capacitance per unit length. It notes that multiplying these two values yields the speed of light, indicating a relationship between electrical properties and wave speed. The conversation suggests that similar principles used to determine wave speed in a string, based on tension and density, could be applied to coaxial cables. Participants are encouraged to explore analogous equations that incorporate capacitance and inductance for modeling wave behavior in coaxial systems. Understanding these relationships is essential for analyzing wave propagation in electrical cables.
Kyuubi
Messages
18
Reaction score
8
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?
 

Attachments

  • IMG_8707.jpg
    IMG_8707.jpg
    22.8 KB · Views: 116
Physics news on Phys.org
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.
 
  • Like
Likes Kyuubi and berkeman
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Thread 'Minimum mass of a block'
Here we know that if block B is going to move up or just be at the verge of moving up ##Mg \sin \theta ## will act downwards and maximum static friction will act downwards ## \mu Mg \cos \theta ## Now what im confused by is how will we know " how quickly" block B reaches its maximum static friction value without any numbers, the suggested solution says that when block A is at its maximum extension, then block B will start to move up but with a certain set of values couldn't block A reach...
Back
Top