Show how to generalize Ampere's circuital law to include the term due to displacement current?

In an Electromagnetic wave propagating along the X - direction, the magnetic field oscillates at a frequency. 5 x 10⁸ Hz and has an amplitude of 10^-7 tesla, acting along the Y-direction.
(i) What is the wavelength of the wave?
(ii) Write the expression representing the corresponding oscillating electric field.

In a plane Electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 1.5 x 10¹⁰Hz with & an amplitude of 36 Vm^-1.
(i) What is the wavelength of a wave?
(ii) What the amplitude of the oscillating magnetic field?
(iii) Straight the average energy density of the electric field \(\left( \overrightarrow { E } \right) \), is equal to average energy density of the magnetic field \(\left( \overrightarrow { B } \right) \)

In an electric circuit, there is a capacitor of reactance 100 Ω connected across the source of 220 V, find the displacement current.

An electromagnetic wave is traveling in vacuum with a speed 3 x 10⁸ m/s. find its velocity in a medium having relative electric and magnetic permeability 2 and 1 respectively.