A plane electromagnetic wave with frequency of 30 MHz travels in free space. At particular point in space and time, electric field is 6 V/m. The magnetic field at this point will be `x xx 10 ^(-8) T.` The value of x is ________

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find the magnetic field (B) corresponding to the given electric field (E) in a plane electromagnetic wave, we can use the relationship between the electric field and magnetic field in free space, which is given by:

\[ B = \frac{E}{c} \]

where:
- \( E \) is the electric field strength (in V/m),
- \( c \) is the speed of light in vacuum, approximately \( 3 \times 10^8 \) m/s.

### Step 1: Identify the given values
- Frequency of the wave: \( f = 30 \text{ MHz} = 30 \times 10^6 \text{ Hz} \)
- Electric field strength: \( E = 6 \text{ V/m} \)

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

### Step 3: Calculate the magnetic field
Using the formula for the magnetic field:
\[ B = \frac{E}{c} \]

Substituting the values:
\[ B = \frac{6 \text{ V/m}}{3 \times 10^8 \text{ m/s}} \]

### Step 4: Perform the calculation
\[ B = \frac{6}{3 \times 10^8} = 2 \times 10^{-8} \text{ T} \]

### Step 5: Identify the value of x
The magnetic field is given in the form \( x \times 10^{-8} \text{ T} \). From our calculation:
\[ B = 2 \times 10^{-8} \text{ T} \]

Thus, comparing with \( x \times 10^{-8} \):
- \( x = 2 \)

### Final Answer
The value of \( x \) is **2**.

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