An electromagnetic wave in vacuum has the electric and magnetic field \mathop E\limits^ \to and \mathop B\limits^ \to , which are always perpendicular to each other. The direction of polarization is given by \mathop X\limits^ \to and that of wave propagation by \mathop k\limits^ \to . Then

\mathop X\limits^ \to ||\mathop E\limits^ \to and \mathop k\limits^ \to ||\mathop E\limits^ \to \times \mathop B\limits^ \to

\mathop X\limits^ \to ||\mathop B\limits^ \to and \mathop X\limits^ \to ||\mathop B\limits^ \to \times \mathop E\limits^ \to

\mathop X\limits^ \to ||\mathop B\limits^ \to and \mathop k\limits^ \to ||\mathop E\limits^ \to \times \mathop B\limits^ \to

\mathop X\limits^ \to ||\mathop E\limits^ \to and \mathop k\limits^ \to ||\mathop B\limits^ \to \times \mathop E\limits^ \to

Electromagnetic Waves PYQ — JEE Main 2012 · Shift 0 · Q50 with Solution

View written solutionFree

Correct answer: B

Key facts about an electromagnetic wave in vacuum

For an electromagnetic wave in vacuum:
- $\vec E \perp \vec B$
- Both $\vec E$ and $\vec B$ are perpendicular to the direction of propagation $\vec k$
- The wave propagates in the direction of the Poynting vector, i.e. $\vec S \propto \vec E \times \vec B$ Hence, $\vec k \parallel \vec E \times \vec B$
Direction of polarization

The polarization of an electromagnetic wave is defined by the direction of the electric field oscillation. Therefore, $\vec X \parallel \vec E$
Check the options
- Option A: $\vec X \parallel \vec B$ and $\vec X \parallel \vec B \times \vec E$
  
  This is wrong because polarization is along $\vec E$ , not along $\vec B$ .
- Option B: $\vec X \parallel \vec E$ and $\vec k \parallel \vec E \times \vec B$
  
  This matches both correct facts.
- Option C: $\vec X \parallel \vec B$ and $\vec k \parallel \vec E \times \vec B$
  
  The second part is correct, but the first part is wrong.
- Option D: $\vec X \parallel \vec E$ and $\vec k \parallel \vec B \times \vec E$
  
  Since $\vec B \times \vec E = -(\vec E \times \vec B),$ this gives the opposite direction to propagation. So this option is wrong.
Final answer

The correct option is: $\boxed{\text{B}}$
Comparison with stored answer

Stored correct answer: B

My derived answer is also B, so they agree.

View written solutionFree

Correct answer: B

Key facts about an electromagnetic wave in vacuum

For an electromagnetic wave in vacuum:
- $\vec E \perp \vec B$
- Both $\vec E$ and $\vec B$ are perpendicular to the direction of propagation $\vec k$
- The wave propagates in the direction of the Poynting vector, i.e. $\vec S \propto \vec E \times \vec B$ Hence, $\vec k \parallel \vec E \times \vec B$
Direction of polarization

The polarization of an electromagnetic wave is defined by the direction of the electric field oscillation. Therefore, $\vec X \parallel \vec E$
Check the options
- Option A: $\vec X \parallel \vec B$ and $\vec X \parallel \vec B \times \vec E$
  
  This is wrong because polarization is along $\vec E$ , not along $\vec B$ .
- Option B: $\vec X \parallel \vec E$ and $\vec k \parallel \vec E \times \vec B$
  
  This matches both correct facts.
- Option C: $\vec X \parallel \vec B$ and $\vec k \parallel \vec E \times \vec B$
  
  The second part is correct, but the first part is wrong.
- Option D: $\vec X \parallel \vec E$ and $\vec k \parallel \vec B \times \vec E$
  
  Since $\vec B \times \vec E = -(\vec E \times \vec B),$ this gives the opposite direction to propagation. So this option is wrong.
Final answer

The correct option is: $\boxed{\text{B}}$
Comparison with stored answer

Stored correct answer: B

My derived answer is also B, so they agree.