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(2E)`

Explanation

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

### Step-by-Step Solution:

1. **Understand the Relationship**: The electric field intensity (E) produced by a source is directly proportional to the power (P) of that source. This can be expressed as:
\[ E \propto P \]

2. **Set Up the Proportionality**: Since the area (A) and distance (r) from the source are constant for both bulbs, we can write:
\[ \frac{E'}{E} = \frac{P'}{P} \]
where:
- \(E'\) is the electric field intensity from the 50W bulb,
- \(E\) is the electric field intensity from the 100W bulb,
- \(P'\) is the power of the 50W bulb (50W),
- \(P\) is the power of the 100W bulb (100W).

3. **Substitute the Values**: Substitute the known values into the equation:
\[ \frac{E'}{E} = \frac{50}{100} \]

4. **Simplify the Equation**: Simplifying the right side gives:
\[ \frac{E'}{E} = \frac{1}{2} \]

5. **Calculate \(E'\)**: Rearranging the equation to find \(E'\):
\[ E' = \frac{E}{2} \]

### Final Result:
The electric field intensity produced by the 50W bulb at a distance of 3m is:
\[ E' = \frac{E}{2} \]