The electrostatic field due to a point charge depends on the distance r as `1/r^2`. Indicate which of the following quantities shows same dependence on r.

Options

A. intensity of light from a point source
B. electrostatic potential due to a point charge
C. electrostatic potential at a distance r from the center of a charged metallic sphere, given rltradius of the sphere
D. none of these

Explanation

To solve the problem, we need to analyze how different quantities depend on the distance \( r \) from a point charge or point source. We are looking for quantities that show the same dependence on \( r \) as the electrostatic field, which varies as \( \frac{1}{r^2} \).

### Step-by-Step Solution:

1. **Understanding the Electrostatic Field**:
The electrostatic field \( E \) due to a point charge \( Q \) at a distance \( r \) is given by the formula:
\[ E = \frac{KQ}{r^2} \]
where \( K \) is a constant. This shows that \( E \) varies as \( \frac{1}{r^2} \).

2. **Analyzing Option A (Intensity of Light)**:
The intensity \( I \) of light from a point source is given by:
\[ I = \frac{S}{4\pi r^2} \]
where \( S \) is the strength of the light source. Here, \( 4\pi \) and \( S \) are constants. Thus, the intensity \( I \) also varies as \( \frac{1}{r^2} \). Therefore, option A shows the same dependence on \( r \) as the electrostatic field.

3. **Analyzing Option B (Electrostatic Potential)**:
The electrostatic potential \( V \) due to a point charge is given by:
\[ V = \frac{KQ}{r} \]
Here, \( V \) varies as \( \frac{1}{r} \), which is not the same as \( \frac{1}{r^2} \). Thus, option B does not show the same dependence.

4. **Analyzing Option C (Electrostatic Potential from a Charged Sphere)**:
For a charged metallic sphere, the electrostatic potential \( V \) at a distance \( r \) from the center (outside the sphere) is also given by:
\[ V = \frac{KQ}{r} \]
Inside the sphere, the potential is constant. Again, this shows a dependence of \( \frac{1}{r} \), not \( \frac{1}{r^2} \). Thus, option C does not show the same dependence.

5. **Conclusion**:
The only quantity that shows the same dependence on \( r \) as the electrostatic field \( E \) is the intensity of light from a point source. Therefore, the correct answer is option A.

### Final Answer:
The quantity that shows the same dependence on \( r \) as the electrostatic field \( E \) is the intensity of light from a point source (Option A).

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