The electric field intensity produced by the radiations coming from 100W bulbs at a 3m distance is E. The electric field intensity produced by the radiations coming from 50W bulb at the same distance is

Options

A. `(E)/(2)`
B. `2E`
C. `(E)/(sqrt(2))`
D. `sqrt(2)E`

Explanation

To solve the problem of finding the electric field intensity produced by the radiation coming from a 50W bulb at a distance of 3m, given that the intensity from a 100W bulb at the same distance is E, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Intensity**:
The intensity (I) of the electric field produced by a point source (like a bulb) at a distance R is given by the formula:
\[ I = \frac{P}{4 \pi R^2} \]
where \( P \) is the power of the source and \( R \) is the distance from the source.

2. **Calculate the Intensity from the 100W Bulb**:
For the 100W bulb at a distance of 3m:
\[ I_{100} = \frac{100}{4 \pi (3)^2} = \frac{100}{36 \pi} \]
We are given that this intensity is equal to E:
\[ E = \frac{100}{36 \pi} \]

3. **Calculate the Intensity from the 50W Bulb**:
Now, for the 50W bulb at the same distance of 3m:
\[ I_{50} = \frac{50}{4 \pi (3)^2} = \frac{50}{36 \pi} \]

4. **Relate the Intensity from the 50W Bulb to E**:
We can express the intensity from the 50W bulb in terms of E:
\[ I_{50} = \frac{50}{36 \pi} = \frac{1}{2} \cdot \frac{100}{36 \pi} = \frac{1}{2} E \]

5. **Final Result**:
Therefore, the electric field intensity produced by the 50W bulb at a distance of 3m is:
\[ I_{50} = \frac{E}{2} \]

### Conclusion:
The electric field intensity produced by the radiation coming from a 50W bulb at a distance of 3m is \( \frac{E}{2} \).

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