For e.m. wave propagating along x-axis, `E_(max)= 30 V//m`. What is the maximum value of magnetic field? 

Options

A. `10^(-7)T`
B. `10^(-8)T`
C. `10^(-9)T`
D. `10^(-6)T`

Answer

To find the maximum value of the magnetic field (B_max) for an electromagnetic wave propagating along the x-axis with a given maximum electric field (E_max), we can use the relationship between the electric field and magnetic field in electromagnetic waves.

### Step-by-Step Solution:

1. **Identify the given values**:
- Maximum electric field (E_max) = 30 V/m
- Speed of light (c) = 3 x 10^8 m/s

2. **Use the relationship between E_max and B_max**:
The relationship between the maximum electric field (E_max) and the maximum magnetic field (B_max) in an electromagnetic wave is given by the equation:
\[ E_{max} = B_{max} \cdot c \]
where:
- E_max is the maximum electric field,
- B_max is the maximum magnetic field,
- c is the speed of light in vacuum.

3. **Rearrange the equation to solve for B_max**:
To find B_max, we can rearrange the equation:
\[ B_{max} = \frac{E_{max}}{c} \]

4. **Substitute the known values**:
Now, substitute the values of E_max and c into the equation:
\[ B_{max} = \frac{30 \, \text{V/m}}{3 \times 10^8 \, \text{m/s}} \]

5. **Calculate B_max**:
Performing the calculation:
\[ B_{max} = \frac{30}{3 \times 10^8} = \frac{30}{3} \times 10^{-8} = 10 \times 10^{-8} = 10^{-7} \, \text{T} \]

6. **Conclusion**:
The maximum value of the magnetic field (B_max) is:
\[ B_{max} = 10^{-7} \, \text{T} \]

### Final Answer:
The maximum value of the magnetic field is \( 10^{-7} \, \text{Tesla} \).

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