The magnetic field in a plane electromagnetic wave is given by: `By=12 xx 10^(-8) sin (1.20 xx 10^7z+3.60 xx 10^(15)t)T.` Calculate the
Speed. of the wave

Answer

To calculate the speed of the electromagnetic wave given the magnetic field equation, we can follow these steps:

### Step 1: Identify the given equation
The magnetic field in the plane electromagnetic wave is given by:
\[ B_y = 12 \times 10^{-8} \sin(1.20 \times 10^7 z + 3.60 \times 10^{15} t) \, T \]

### Step 2: Identify the parameters
From the equation, we can identify:
- The wave number \( k = 1.20 \times 10^7 \, \text{m}^{-1} \)
- The angular frequency \( \omega = 3.60 \times 10^{15} \, \text{s}^{-1} \)

### Step 3: Use the formula for speed of the wave
The speed \( v \) of an electromagnetic wave can be calculated using the formula:
\[ v = \frac{\omega}{k} \]

### Step 4: Substitute the values
Substituting the identified values into the formula:
\[ v = \frac{3.60 \times 10^{15}}{1.20 \times 10^{7}} \]

### Step 5: Perform the calculation
Calculating the speed:
\[ v = \frac{3.60}{1.20} \times 10^{15 - 7} \]
\[ v = 3.00 \times 10^{8} \, \text{m/s} \]

### Conclusion
The speed of the electromagnetic wave is:
\[ v = 3.00 \times 10^{8} \, \text{m/s} \]

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