What is the correct expression of the speed of the electromagnetic wave ?

Options

A. `v=w/k`
B. `v=(w)/(kl)`
C. `v=(wl)/(k)`
D. `v=(wq)/(k)`

Explanation

To find the correct expression for the speed of an electromagnetic wave, we can follow these steps:

### Step 1: Understand the wave equation
The electromagnetic wave can be represented by the electric field \( E \) and magnetic field \( B \). The general form of the wave equation for the electric field is:
\[ E = E_0 \sin(kx - \omega t) \]
and for the magnetic field:
\[ B = B_0 \sin(kx - \omega t) \]
where:
- \( E_0 \) and \( B_0 \) are the amplitudes of the electric and magnetic fields, respectively,
- \( k \) is the wave number,
- \( \omega \) is the angular frequency,
- \( x \) is the position,
- \( t \) is the time.

### Step 2: Identify the coefficients
In the wave equation \( E = E_0 \sin(kx - \omega t) \), the coefficient of \( t \) is \( -\omega \) and the coefficient of \( x \) is \( k \).

### Step 3: Determine the speed of the wave
The speed \( v \) of the wave can be calculated using the formula:
\[ v = -\frac{\text{coefficient of } t}{\text{coefficient of } x} \]
Substituting the coefficients:
\[ v = -\frac{-\omega}{k} = \frac{\omega}{k} \]

### Step 4: Conclusion
Thus, the correct expression for the speed of the electromagnetic wave is:
\[ v = \frac{\omega}{k} \]

### Final Answer
The correct option is:
\[ \text{Option 1: } v = \frac{\omega}{k} \]

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