A certain transmission line (very long) is constructed from two thin metal plates (parallel to each other) of width b, which are separated by a very small distance ‘h’ lt lt ‘b’ . The current travels down one strip and back along the other, and it is distributed uniformly over the surface of the plates as shown in figure. Neglect fringing field at ends of plates.

Self inductance per unit length of combination is (c is speed of light)

Options

A. `b/(epsilon_(0)c^(2)h)`
B. `(c^(2)h)/(epsilon_(0)b)`
C. `h/(epsilon_(0)c^(2)b)`
D. `(c^(2)b)/(epsilon_(0)h)`

Explanation

Considering length of line is
`E=(sigma)/(epsilon_(0))rArr V=Eh`
`V=(sigma)/(epsilon_(0))h=Q/(epsilon_(0)bl).h=c=Q/v`
`C=(epsilon_(0)bl)/h`
`C/l=(epsilon_(0)b)/h`
`rArr B=(mu_(0)K)/2+(mu_(0)K)/2=mu_(0)K=(mu_(0)I)/b` (K=current per unit width)
`vec(B)=(mu_(0)I)/b(-hatk)`

Consider a rectangular surface as shown in the figure.
Now `phi=Bvl`
`phi=(mu_(0)I)/b.h l =LI`
`L=(mu_(0)hl)/b`
`L/l=(mu_(0)h)/b` But
`c=1/(sqrt(mu_(0)epsilon_(0)))`
`c^(2)=1/(sqrt(mu_(0)epsilon_(0)))`
`mu_(0)=1/(epsilon_(0)c^(2))`
`L/l=h/(epsilon_(0)c^(2)b)`