A plane electromagnetic wave propagates along the direction in free space. The components of the electric field and magnetic field vectors associated with the wave in Cartesian frame are:
- A
- B
- C
- D
A plane electromagnetic wave propagates along the direction in free space. The components of the electric field and magnetic field vectors associated with the wave in Cartesian frame are:
Correct answer:B
Standard Method
Given: A plane electromagnetic wave propagates along the direction in free space.
Find: The correct components of and in the Cartesian frame.
In an electromagnetic wave, the electric field, magnetic field, and direction of propagation are mutually perpendicular to each other.
Since the wave propagates along the -axis, both and must lie in the plane perpendicular to the -axis.
For the stated orientation,
Hence, the correct field components are and .
Therefore, the correct option is B.
Using Mutual Perpendicularity
Given: The direction of propagation is .
Find: Which pair of field components can represent the electric and magnetic fields.
A plane electromagnetic wave satisfies the perpendicular relation among three directions:
Because propagation is along , neither field can have an -component in the required pair.
So options containing or are not suitable. The remaining consistent transverse arrangement is with .
Therefore, the correct answer is , which corresponds to option B.
Choosing components containing or . This is wrong because electromagnetic waves are transverse in free space, so both fields are perpendicular to the direction of propagation. Instead, choose field components only along directions perpendicular to .
Assuming any two perpendicular components are acceptable without checking the propagation direction. This is wrong because the field directions must be perpendicular to each other and to the direction of motion. First fix propagation along , then assign transverse components.
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