1) A loss-less coaxial transmission line uses an insulating dielectric material with Er = 9. The radii of the cylindrical conductors are 0.5 cm and 1 cm. Assume a square voltage pulse of magnitude 50 V is sent down the line which is in the z direction.
(a) What is the impedance of the transmission line?
(b) How fast is the voltage pulse moving down the line?
(c) What is magnitude and direction of the electric field inside the pulse?
(d) What is the charge density (ps) on the inner conductor?
(e) As the pulse moves down the wire the charge on the surface is also moving with the pulse.Calculate the current density on the surface of the wire from Js = (ps)(u) where the magnitude of u was determined in (b).
(f) Calculate the current flowing on the inner wire resulting from the moving charge in the voltage pulse.
(g) Show the ratio of the magnitude of the voltage (50 V) and current (from (f) ) gives you the impedance calculated in (a).
(h) Use the current calculated in (f) to calculated the magnetic field in the transmission line in the region of the voltage pulse (you can assume calculating the magnetic field that it is field from a wire that is infinitely long).
(i) Show that ????̂ × ????̂ gives a propagation direction along the transmission line.
(j) Calculate the ratio of the electric field to the magnetic field in the space between the conductors
(k) Show that the answer to (j) is what you would expect for an electromagnetic wave propagating in a dielectric with Er = 9