A plane electromagnetic wave of frequency 28 MHz travels in free space along the positive x-direction . At a particular point in space and time, electric field is 9.3 V/m along positive y-direction. The magnetic field (in T) at that point is

Options

A. `3.1 xx 10^(-8)` along positive z-direction
B. `3.1 xx 10^(-8)` along negative z-direction
C. `3.2 xx 10^(7)` along positive z-direction
D. `3.2 xx 10^7` along negative z-direction

Answer

To find the magnetic field at a point where the electric field of a plane electromagnetic wave is given, we can use the relationship between the electric field (E) and the magnetic field (B) in an electromagnetic wave.

### Step-by-Step Solution:

1. **Identify the given values:**
- Frequency of the wave, \( f = 28 \text{ MHz} = 28 \times 10^6 \text{ Hz} \)
- Electric field strength, \( E = 9.3 \text{ V/m} \)
- Speed of light in vacuum, \( c = 3 \times 10^8 \text{ m/s} \)

2. **Use the relationship between electric field and magnetic field:**
The relationship between the electric field \( E \) and the magnetic field \( B \) in an electromagnetic wave is given by:
\[ c = \frac{E}{B} \]
Rearranging this gives:
\[ B = \frac{E}{c} \]

3. **Substitute the known values into the equation:**
\[ B = \frac{9.3 \text{ V/m}}{3 \times 10^8 \text{ m/s}} \]

4. **Calculate the magnetic field:**
\[ B = 3.1 \times 10^{-8} \text{ T} \]

5. **Determine the direction of the magnetic field:**
The electric field is in the positive y-direction, and the wave is propagating in the positive x-direction. According to the right-hand rule for electromagnetic waves, the magnetic field will be in the positive z-direction.

### Final Answer:
The magnetic field at that point is \( 3.1 \times 10^{-8} \text{ T} \) in the positive z-direction.

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