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 (B) at a point in space where an electromagnetic wave is present, we can use the relationship between the electric field (E) and the magnetic field in electromagnetic waves. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Frequency of the electromagnetic wave, \( f = 28 \text{ MHz} = 28 \times 10^6 \text{ Hz} \)
- Electric field strength, \( E = 9.3 \text{ V/m} \)

2. **Determine the Speed of Light (C)**:
- The speed of light in free space is a constant, \( C = 3 \times 10^8 \text{ m/s} \).

3. **Use the Relationship Between E and B**:
- For electromagnetic waves, the relationship between the electric field (E) and the magnetic field (B) is given by:
\[ \frac{E}{B} = C \]
- Rearranging this equation gives:
\[ B = \frac{E}{C} \]

4. **Substitute the Known Values**:
- Substitute the values of E and C into the equation:
\[ B = \frac{9.3 \text{ V/m}}{3 \times 10^8 \text{ m/s}} \]

5. **Calculate B**:
- Performing the calculation:
\[ B = \frac{9.3}{3 \times 10^8} = 3.1 \times 10^{-8} \text{ T} \]

6. **Determine the Direction of B**:
- Since the electric field is in the positive y-direction and the wave is traveling in the positive x-direction, the magnetic field will be in the positive z-direction (using the right-hand rule).

7. **Final Answer**:
- The magnetic field at that point is:
\[ B = 3.1 \times 10^{-8} \text{ T} \text{ in the positive z-direction} \]