Question

Depict the variation of electric field `vecE` and magnetic field `vecB` with respect to the direction of propagation of an electromagnetic wave. Write their two important characteristics.

Answer 1

An electromagnetic (EM) wave consists of time-varying electric and magnetic fields that propagate through space, perpendicular to each other and the direction of wave propagation.

Variation of `vecE` and `vecB`:

1. Sinusoidal Oscillations: Both the electric field `vecE` and the magnetic field `vecB` oscillate sinusoidally as the wave propagates.
2. Mutual Perpendicularity: The electric field `vecE` and the magnetic field `vecB` are mutually perpendicular to each other.
3. Perpendicular to Propagation: Both `vecE` and `vecB` are perpendicular to the direction of wave propagation. When the wave propagates along the x-axis:
   • The electric field `vecE` oscillates along the y-axis.
   • The magnetic field `vecE` oscillates along the z-axis.

Mathematically, the wave can be expressed as:

E = E₀ sin(kx − ωt)

B = B₀ sin(kx − ωt)

Two Important Characteristics of EM Waves:

1. Transverse Nature: EM waves are transverse waves, meaning the electric and magnetic fields oscillate perpendicular to the direction of propagation.
2. In-phase Oscillations: The electric field `vecE`and magnetic field `vecB` reach their maxima and minima simultaneously.

Other Properties of EM Waves:

• Do not require a material medium: EM waves can propagate through a vacuum, unlike mechanical waves, which require a medium.
• Carry energy and momentum: EM waves carry energy and momentum, allowing them to transfer both through space.