Question

A coaxial cable has length d, inner wire radius a and outer shell radius b. You can regard its capacitance and inductance to be in series. If charge +q is placed on the inner wire with −q on the outer shell, how much time will elapse before you will find −q on the inner wire and +q on the outer shell?

Answer 1

Given,

Length of the coaxial cable is d, inner radius is a, and outer radius is b

Now,

For coaxial cable, inductance of a cable of length d is given as,    L =

For coaxial cable, capacitance of the cable of length d is given as, C =

Now,

resonant frequency of a LC circuit is given as, = 1 /

Now,

equivalent frequency, f₀ = / 2

Now,

Since, frequency = 1 / Time period

=> time period, T = 1 / f₀

                              = 2/ = 2

                              = 2

                              = 2

                              = 2d

Or   time elapsed is 2d