True or false: (a) maxwell's equations apply only to fields that are constant over time.(b) the wave equation can be derived from maxwell's equations.(c) electromagnetic waves are transverse waves.(d) in an electromagnetic wave in free space, the electric and magnetic fields are in phase.(e) in an electromagnetic wave in free space, the ratio of the magnitudes of electric and magnetic field vectors e and b is equal to c (speed of ) in an electromagnetic wave in free space, the electric and magnetic energy densities are equal.

(a) False

(b) True

(c) True

(d) True

(e) True

(f) True

Explanation:

(a) Maxwell's equations not only applies to constant fields but it applies to both the fields, i.e., Time variant field as well as Time Invariant field.

(b) We make use of the Modified form of the Ampere's law and Faraday's Law to derive the wave equation.

(c) Electromagnetic waves contains both the electric and magnetic fields and these fields oscillates at an angle of to the direction of wave propagation.

(d) In free space both the electric and magnetic fields are in phase while considering electromagnetic waves.

(e) In free space or vacuum, the expression for the speed of light in terms of electric and magnetic field is given as:

Thus the ratio of the magnitudes of the electric and magnetic field vectors are equal to the speed of light in free space.

(f) In free space or in vacuum the energy density of the electromagnetic wave is divided equally in both the fields and hence are equal.