A plane electromagnetic wave of frequency `20 MHz` travels through a space along x-direction. If the electric field vector at a certain point in space is `6 Vm^(-1)`,then what is the magnetic field vector at that point?

Options

A. `2 xx 10^(-8) T`
B. `1/2 xx 10^(-8) T`
C. `2T`
D. `1/2 T`

Explanation

To find the magnetic field vector corresponding to the given electric field vector in a plane electromagnetic wave, we can follow these steps:

### Step 1: Identify the given data
We have the following information:
- Frequency of the electromagnetic wave, \( f = 20 \, \text{MHz} = 20 \times 10^6 \, \text{Hz} \)
- Electric field vector, \( E = 6 \, \text{V/m} \)

### Step 2: Calculate the speed of light
The speed of light in a vacuum is a constant, given by:
\[ c = 3 \times 10^8 \, \text{m/s} \]

### Step 3: Use the relationship between electric field and magnetic field
In an electromagnetic wave, the relationship between the electric field \( E \) and the magnetic field \( B \) is given by:
\[ c = \frac{E}{B} \]
From this, we can rearrange the formula to find the magnetic field \( B \):
\[ B = \frac{E}{c} \]

### Step 4: Substitute the known values into the equation
Now, we can substitute the values of \( E \) and \( c \) into the equation:
\[ B = \frac{6 \, \text{V/m}}{3 \times 10^8 \, \text{m/s}} \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ B = \frac{6}{3 \times 10^8} = 2 \times 10^{-8} \, \text{T} \]

### Step 6: Conclusion
Thus, the magnetic field vector at that point is:
\[ B = 2 \times 10^{-8} \, \text{T} \]

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