Problem 2150 - JEE Physics

Question

The electric and magnetic field of an electromagnetic wave are (A) in phase and perpendicular to each other (B) in phase and parallel to each other (C) in opposite phase and perpendicular to each other (D) in opposite phase and parallel to each other

Step-by-Step Solution

Answer

The electric and magnetic fields in an electromagnetic wave are in phase and perpendicular to each other. Therefore, the correct answer is (A) in phase and perpendicular to each other.

Step 1: Understand the properties of electromagnetic waves

Electromagnetic waves are waves that consist of oscillating electric and magnetic fields, which are perpendicular to each other and the direction of wave propagation. The electric field (E-field) and magnetic field (B-field) in an electromagnetic wave always maintain a fixed phase relationship.

Step 2: Analyze the phase relationship between the electric and magnetic fields

In an electromagnetic wave, the electric and magnetic fields oscillate sinusoidally and are always in phase with one another. This means that their peaks and troughs occur simultaneously, and the phase difference between them is zero.

Step 3: Analyze the direction relationship between the electric and magnetic fields

In an electromagnetic wave, the electric field and the magnetic field are always perpendicular to each other. This is because the wave propagates in the direction that is perpendicular to both fields. If they were parallel, it would contradict the nature of electromagnetic waves.

Step 4: Choose the correct answer based on the analysis

Based on our analysis in Steps 2 and 3, we know that the electric and magnetic fields in an electromagnetic wave are in phase and perpendicular to each other. Therefore, the correct answer is: (A) in phase and perpendicular to each other.

Key Concepts

Electric Field

In an electromagnetic wave, the electric field is a fundamental component that oscillates in space and time. This field is represented by the symbol \( \,E\) and is crucial in determining how the wave interacts with charged particles. An electric field is a vector field, meaning it has both magnitude and direction.
The electric field in an electromagnetic wave changes over time, following a sinusoidal pattern. As the wave moves through space, the electric field vector points in different directions perpendicular to the direction of wave propagation. This alternating nature is essential for the wave's energy transfer.

• The electric field magnitude determines the wave's intensity.
• The direction of the electric field influences how it affects charged objects in its path.

Understanding the oscillatory behavior of the electric field helps in grasping the dynamic nature of electromagnetic waves.

Magnetic Field

Complementing the electric field, the magnetic field is another vital element of electromagnetic waves. Represented by \( \,B\), this field also oscillates sinusoidally but perpendicular to the electric field. The magnetic field plays a significant role in the wave's characteristics and behaviors.
The magnetic field, like the electric field, is a vector. Its direction is also perpendicular to both the electric field and the direction of wave propagation. This relationship ensures the effective propagation of electromagnetic energy through space. Some key points about the magnetic field in electromagnetic waves are:

• The magnetic field magnitude is directly proportional to the electric field magnitude.
• It exerts force on moving charges, contributing to the overall dynamics of the wave interaction.

By exploring the oscillatory nature and orientation of the magnetic field, students gain deeper insights into electromagnetic wave propagation.

Wave Propagation

Wave propagation is the process by which electromagnetic waves travel through space. These waves are capable of moving through a vacuum without the need for a medium, unlike sound waves, which require air or another medium. The direction of wave propagation is determined by the right-hand rule, where the thumb points in the direction of wave travel, and the thumb, index, and middle fingers represent the directions of the magnetic field, electric field, and wave propagation, respectively.
Electromagnetic waves propagate by transmitting energy through the oscillating electric and magnetic fields. Key aspects include:

• The speed of electromagnetic waves is constant in a vacuum and equals the speed of light, \( c = 3 \, \times \, 10^8 \, \text{m/s} \).
• Wave propagation direction is orthogonal to both the electric and magnetic fields.

This self-perpetuating mechanism of wave propagation is what enables electromagnetic signals to traverse vast distances, such as the immense reaches of space.

Phase Relationship

The phase relationship between the electric and magnetic fields in an electromagnetic wave is essential to understanding their synchronous behavior. Both fields are in phase, meaning they oscillate together and reach their peaks and troughs simultaneously. This synchronized oscillation ensures that certain properties of the wave, such as direction and consistency, are maintained.
Phase relationships are defined by the angle of lead or lag between two oscillating quantities. In electromagnetic waves, the phase angle between the electric and magnetic fields is zero, confirming they are in phase. Important points about phase relationship include:

• The zero-phase difference ensures maximum energy is transferred without cancellation.
• In-phase fields maintain the wave's structural integrity as it propagates.

Grasping the concept of phase relationship is vital for analyzing how electromagnetic waves propagate and interact with different environments.