Question

At some time t the time-varying magnetic field component of an electromagnetic wave is pointed in the -xˆ direction. If the electromagnetic wave velocity is in the -zˆ direction, what is the direction of the time-varying electric field component of this wave at t?

Please explain the reasoning behind the answer

A. yˆ

B. -yˆ

C. -zˆ

D. zˆ

Answer 1

Electromagnetic (EM) waves are changing electric and magnetic fields, transporting energy and momentum through space. EM waves are solutions of Maxwell's equations, which are the fundamental equations of electrodynamics. EM waves require no medium, they can travel through empty space. Sinusoidal plane waves are one type of electromagnetic waves. Not all EM waves are sinusoidal plane waves, but all electromagnetic waves can be viewed as a linear superposition of sinusoidal plane waves traveling in arbitrary directions. A plane EM wave traveling in the x-direction is of the form

E(x,t) = Emaxcos(kx - ωt + φ),  B(x,t) = Bmaxcos(kx - ωt + φ). E is the electric field vector, and B is the magnetic field vector of the EM wave. For electromagnetic waves E and B are always perpendicular to each other and perpendicular to the direction of propagation. The direction of propagation is the direction of E x B. If, for a wave traveling in the x-direction E = Ej, then B = Bk and j x k = i. Electromagnetic waves are transverse waves. Now we have given is that, the direction of magnetic field component at time "t" is in -x direction and the wave velocity is in "-z" direction. we know that cross product of electric field component direction and magnetic field component direction gives us the direction of propagation , means we already know the direction of propagation which is in -z direction, therefore to satisafy the given condition the magnetic field component must be in "-y " direction. Thus the electric field component of EM wave at time "t" is in "-y" direction, hence the option B is correct answer