Problem 2185 - JEE Physics

Question

The oscillating electric and magnetic field vectors of an electromagnetic waves far away from source are oriented along (A) Mutually perpendicular direction and differ in phase by \(90^{\circ}\) (B) Mutually perpendicular and in same phase (C) In same direction and in same phase (D) In same direction and differ in phase by \(90^{\circ}\)

Step-by-Step Solution

Answer

The correct answer is (B) Mutually perpendicular and in same phase. This is because the electric and magnetic field vectors in electromagnetic waves are always perpendicular to each other, and they oscillate in phase.

Step 1: Determine the properties of electromagnetic waves

Electromagnetic waves are waves composed of oscillating electric and magnetic fields. These waves are produced by time-varying electric and magnetic fields, which are always mutually perpendicular to each other. Also, the direction of wave propagation is perpendicular to both field vectors.

Step 2: Understand the relation between the electric and magnetic fields

In electromagnetic waves, the electric field (E) and the magnetic field (B) are in phase, meaning they both reach their maximum and minimum values simultaneously. Far away from the source, electromagnetic waves usually follow the properties of plane waves. This implies that the electric and magnetic fields maintain their mutual perpendicular orientation and in-phase relationship as the electromagnetic wave propagates through space.

Step 3: Choose the correct option

Based on the properties of electromagnetic waves and the relationship between the electric and magnetic fields, we can conclude that the correct answer is: (B) Mutually perpendicular and in same phase. This is because the electric and magnetic field vectors are always perpendicular to each other, and they oscillate in phase in an electromagnetic wave.

Key Concepts

Electric and Magnetic Fields

Electromagnetic waves are made up of electric ( E ) and magnetic ( B ) fields. These fields oscillate, or move back and forth. Each field has a certain direction and strength, which are represented by vectors. In electromagnetic waves, these two vectors are always mutually perpendicular. This means they form a 90-degree angle with each other.
Understanding this orientation is key.

• The electric field vector, E , represents the direction and strength of the electric force.
• The magnetic field vector, B , represents the direction and strength of the magnetic force.

Both fields not only oscillate, but they do so in conjunction, ensuring that the wave maintains a consistent nature as it travels through space.
This mutual perpendicularity ensures that the electromagnetic wave carries energy effectively through a vacuum, such as outer space. While oscillating, E and B vectors reach their peak and zero values at the same times, meaning they are "in phase." This synchronized movement is essential for the properties of electromagnetic waves.

Wave Propagation

Wave propagation is the process by which waves travel through a medium or space. For electromagnetic waves, this travel occurs even in a vacuum—without needing a material medium. The critical aspect of wave propagation is how these waves move forward.
In electromagnetic waves:

• The electric and magnetic fields oscillate perpendicular to each other and the direction the wave travels.
• The direction of wave propagation is perpendicular to both the electric and magnetic fields.

This characteristic three-way perpendicular relationship enables the wave to carry energy through space efficiently.
The wave propagation occurs due to changing electric and magnetic fields. As E changes, it creates a change in B , and vice versa. This consistent change and generation of fields propel the wave forward. The energy launched from the source continues on this path as the fields fluctuate, carrying electromagnetic energy over vast distances.

Plane Waves

A plane wave is a simplified model describing electromagnetic waves that travel in a uniform direction. Far from their source, electromagnetic waves often behave as plane waves due to decreased influences from their origin.
Plane waves are crucial in physics because they help simplify complex behaviors into understandable concepts:

• In an electromagnetic plane wave, both electric and magnetic fields remain constant in direction and magnitude on any plane perpendicular to the direction of propagation.
• They maintain the in-phase and mutual perpendicular relationship between electric and magnetic fields.

By maintaining consistency as they propagate, plane waves provide an excellent framework for understanding more complex wave patterns.
For instance, light from the Sun can be approximated as behaving like a plane wave when it reaches Earth, since it has spread out significantly from its origin. This simplicity allows easier problem-solving and comprehension of wave behavior at various times and locations.