Question

If \(E\) and \(B\) are the magnitudes of the electric and magnetic fields respectively of a plane electromagnetic wave and \(\omega\) is its angular frequency, then the wavelength of the wave is

• A. \(\dfrac{\pi E}{\omega B}\)
• B. \(\dfrac{2\pi E}{\omega B}\)
• C. \(\dfrac{E}{2\pi\omega B}\)
• D. \(\dfrac{E}{\pi\omega B}\)

Hint:

For an electromagnetic wave, \[ \boxed{ \frac{E}{B}=c } \] and \[ \boxed{ \lambda=\frac{2\pi c}{\omega}. } \] Combining these, \[ \boxed{ \lambda=\frac{2\pi E}{\omega B}. } \]

Answer 1

The Correct Option is B

Step 1: Use the relation between electric and magnetic fields. For an electromagnetic wave, \[ \frac{E}{B} = c. \] Also, \[ c=\nu\lambda. \] Since \[ \omega=2\pi\nu, \] we have \[ \nu=\frac{\omega}{2\pi}. \]

Step 2: Calculate the wavelength. \[ \lambda = \frac{c}{\nu} = \frac{E/B}{\omega/(2\pi)} = \frac{2\pi E}{\omega B}. \] Hence, \[ \boxed{ \lambda=\frac{2\pi E}{\omega B} } \] Therefore, \[ \boxed{(B)} \] is the correct answer.