Question

In an electromagnetic wave, the electric field ($\vec{E}$) and the magnetic field ($\vec{B}$) oscillate along x-axis and y-axis respectively. The wave is propagating along:

• A. $z$-axis
• B. $-z$-axis
• C. $x$-axis
• D. $-y$-axis

Hint:

The wave travels along \(\vec E\times\vec B\). For E along x and B along y, this is along +z.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
An electromagnetic wave is transverse. The electric field \(\vec E\), the magnetic field \(\vec B\) and the direction of travel are mutually perpendicular. The wave travels along the direction of \(\vec E\times\vec B\).

Step 2: Key Formula or Approach:
The direction of propagation is given by \(\hat n=\hat E\times\hat B\).

Step 3: Detailed Explanation:
Here \(\vec E\) oscillates along the x-axis and \(\vec B\) along the y-axis. So we take the cross product of the unit vectors: \[ \hat i\times\hat j=\hat k \]
So the wave moves along the +z axis. This follows the cyclic rule \(\hat i\times\hat j=\hat k\), \(\hat j\times\hat k=\hat i\), \(\hat k\times\hat i=\hat j\).

Step 4: Why the other options are wrong:
The \(-z\) axis would need \(\vec E\times\vec B\) to point along \(-\hat k\), which happens only if one field is reversed. The x-axis is the direction of \(\vec E\) itself. The \(-y\) axis lies along \(\vec B\). A transverse wave cannot move along either of its own field directions.

Final Answer:
The wave propagates along the z-axis, which is option (A). \[ \boxed{+z\text{ axis}} \]