Manitude of the electric and magnetic field in an electromagnetic wave radiated by a `200 W` bulb at a distance 2m from it is assuming efficiency of bulb is `5%` and it behaves like a point source.

Options

A. `12.27 N//C, 4.09 xx 10^(-8) T`
B. `10 N//C, 10^(-5) T`
C. `11.7 N//C, 5 xx 10^(-6)T`
D. `5N//C, 10^(-4)T`

Explanation

To find the magnitude of the electric and magnetic fields in an electromagnetic wave radiated by a 200 W bulb at a distance of 2 m, we can follow these steps:

### Step 1: Calculate the Effective Power
The bulb has an efficiency of 5%. Therefore, the effective power (P) radiated by the bulb can be calculated as:
\[ P = \text{Efficiency} \times \text{Total Power} = \frac{5}{100} \times 200 \, \text{W} = 10 \, \text{W} \]

### Step 2: Calculate the Intensity of the Wave
The intensity (I) of the electromagnetic wave at a distance (r) from a point source is given by:
\[ I = \frac{P}{A} = \frac{P}{4\pi r^2} \]
Substituting the values:
\[ I = \frac{10}{4\pi(2^2)} = \frac{10}{4\pi(4)} = \frac{10}{16\pi} \]
Using \(\pi \approx 3.142\):
\[ I \approx \frac{10}{16 \times 3.142} \approx \frac{10}{50.272} \approx 0.199 \, \text{W/m}^2 \]

### Step 3: Calculate the Maximum Electric Field (E₀)
The intensity is also related to the electric field by the formula:
\[ I = \frac{1}{2} \epsilon_0 c E_0^2 \]
Rearranging for \(E_0\):
\[ E_0^2 = \frac{2I}{\epsilon_0 c} \]
Taking the square root:
\[ E_0 = \sqrt{\frac{2I}{\epsilon_0 c}} \]
Substituting the known values (where \(\epsilon_0 \approx 8.85 \times 10^{-12} \, \text{F/m}\) and \(c \approx 3 \times 10^8 \, \text{m/s}\)):
\[ E_0 = \sqrt{\frac{2 \times 0.199}{(8.85 \times 10^{-12})(3 \times 10^8)}} \]
Calculating:
\[ E_0 = \sqrt{\frac{0.398}{2.655 \times 10^{-3}}} \approx \sqrt{150.0} \approx 12.27 \, \text{N/C} \]

### Step 4: Calculate the Maximum Magnetic Field (B₀)
The relationship between the electric field and magnetic field in an electromagnetic wave is given by:
\[ B_0 = \frac{E_0}{c} \]
Substituting the values:
\[ B_0 = \frac{12.27}{3 \times 10^8} \approx 4.09 \times 10^{-8} \, \text{T} \]

### Final Results
- Maximum Electric Field (E₀) = 12.27 N/C
- Maximum Magnetic Field (B₀) = \(4.09 \times 10^{-8}\) T