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Question

The electric field E and magnetic field B in an electromagnetic wave are related. In a vacuum, which of the following is true?

VENKATESWARARAO · Accepted Answer

## CORE INFORMATION
✓ **Answer**: D
## CONCEPT FRAMEWORK
 **Primary Concept**: Electromagnetic waves
 **Related Topics**: Maxwell's equations, wave propagation
 **Prerequisites**: Understanding of electric and magnetic fields, vectors
## SOLUTION PATHWAY
**Given Information**:
  Electromagnetic wave in a vacuum.
  Electric field E and Magnetic field B.
**Method & Steps**:
 1. Understand the nature of electromagnetic waves.
  Reasoning: Electromagnetic waves are transverse waves, meaning the oscillations of the electric and magnetic fields are perpendicular to the direction of wave propagation.
  Formula/Rule: None directly applicable, but understanding the transverse nature is key.
 2. Consider the relationship between E and B.
  Working: In a vacuum, the electric and magnetic fields are perpendicular to each other.  This is a fundamental property of electromagnetic waves. The magnitudes are related by $c = \frac{E}{B}$, where c is the speed of light.
  Key Point: The direction of propagation is given by the cross product of E and B:  $\vec{S} = \frac{1}{\mu_0} \vec{E} 	imes \vec{B}$, where $\vec{S}$ is the Poynting vector representing the direction of energy flow (propagation).
 3. Analyze the options.
  Result: Option D correctly states that E and B are perpendicular to each other and to the direction of propagation.
  Verification: This aligns with the fundamental properties of electromagnetic waves and the relationship between E, B, and the direction of propagation.
 ## OPTION ANALYSIS
A :x: E and B are not parallel to each other or the direction of propagation in an electromagnetic wave.
B :x: E and B are perpendicular to each other, but not parallel to the direction of propagation.
 C :x: E and B are not parallel to each other. They are perpendicular in an electromagnetic wave.
D ✓: This option correctly describes the relationship between E, B, and the direction of propagation in an electromagnetic wave in a vacuum.  E and B are mutually perpendicular and both are perpendicular to the direction of wave propagation.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing longitudinal and transverse waves: Electromagnetic waves are transverse, not longitudinal.
  2.Incorrectly relating the direction of E and B to the direction of propagation: They are perpendicular, not parallel.
 **Quick Tips**:
  1.Remember the right-hand rule: Use the right-hand rule to determine the direction of propagation from the directions of E and B using the Poynting vector.
  2.Visualize the wave:  Imagine a wave with E and B oscillating perpendicularly to each other and to the direction of travel.

VENKATESWARARAO · Answer

E and B are parallel to each other and to the direction of propagation.

VENKATESWARARAO · Answer

E and B are perpendicular to each other but parallel to the direction of propagation.

VENKATESWARARAO · Answer

E and B are parallel to each other and perpendicular to the direction of propagation.

VENKATESWARARAO · Answer

The correct Option is "E and B are perpendicular to each other and to the direction of propagation."

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