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

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 (`vecB`) 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.