The magnetic field of an electromagnetic wave is given by
`3 xx 10^(-7) sin (10^(3) x + 6.28 xx 10^(12)t ).` The wave length of the electromagnetic wave is

Options

A. 6.28 cm
B. 3.14 cm
C. 0.63 cm
D. 0.32 cm

Explanation

To find the wavelength of the given electromagnetic wave, we can follow these steps:

### Step 1: Identify the wave equation
The magnetic field of the electromagnetic wave is given by:
\[ B = 3 \times 10^{-7} \sin(10^{3} x + 6.28 \times 10^{12} t) \]

### Step 2: Compare with the standard wave equation
The standard form of a wave equation is:
\[ B = B_0 \sin(kx + \omega t) \]
where:
- \( B_0 \) is the amplitude,
- \( k \) is the wave number,
- \( \omega \) is the angular frequency.

From the given equation, we can identify:
- \( k = 10^{3} \)
- \( \omega = 6.28 \times 10^{12} \)

### Step 3: Relate wave number to wavelength
The wave number \( k \) is related to the wavelength \( \lambda \) by the equation:
\[ k = \frac{2\pi}{\lambda} \]

### Step 4: Solve for wavelength
Substituting the value of \( k \):
\[ 10^{3} = \frac{2\pi}{\lambda} \]

Now, rearranging to find \( \lambda \):
\[ \lambda = \frac{2\pi}{10^{3}} \]

### Step 5: Calculate the wavelength
Calculating \( \lambda \):
\[ \lambda = \frac{2 \times 3.14}{10^{3}} \]
\[ \lambda \approx \frac{6.28}{10^{3}} \]
\[ \lambda \approx 6.28 \times 10^{-3} \, \text{meters} \]

### Step 6: Convert to centimeters
Since \( 1 \, \text{meter} = 100 \, \text{centimeters} \):
\[ \lambda \approx 6.28 \times 10^{-3} \, \text{meters} \times 100 \, \text{cm/m} \]
\[ \lambda \approx 0.628 \, \text{cm} \]

### Final Answer
Thus, the wavelength of the electromagnetic wave is approximately:
\[ \lambda \approx 0.63 \, \text{cm} \]