A charged spherical conductor of radius R carries a charge Q. a point charge q is placed at an outside point at a distance x from the surface of the sphere. The force experienced by the point charge will be proportional to

Options

A. `1/x^(2)`
B. `(R+x)^(2)`
C. `(1)/((R+x)^(2))`
D. `(1)/((R-x)^(2))`

Explanation

To solve the problem, we need to determine the force experienced by a point charge \( q \) placed outside a charged spherical conductor of radius \( R \) that carries a charge \( Q \). The point charge is located at a distance \( x \) from the surface of the sphere.

### Step-by-Step Solution:

1. **Identify the Total Distance**:
The distance from the center of the spherical conductor to the point charge \( q \) is given by the sum of the radius of the sphere \( R \) and the distance \( x \) from the surface of the sphere to the point charge. Therefore, the total distance \( d \) from the center of the sphere to the point charge is:
\[ d = R + x \]

**Hint**: Remember that the total distance includes both the radius of the sphere and the distance from the surface to the point charge.

2. **Understand the Nature of the Force**:
The force \( F \) experienced by the point charge \( q \) due to the charge \( Q \) on the spherical conductor can be described by Coulomb's law. According to Coulomb's law, the force between two point charges is inversely proportional to the square of the distance between them:
\[ F \propto \frac{1}{d^2} \]

**Hint**: Recall that the force between two charges decreases with the square of the distance between them.

3. **Substitute the Total Distance**:
Since we have established that \( d = R + x \), we can substitute this into the expression for the force:
\[ F \propto \frac{1}{(R + x)^2} \]

**Hint**: Make sure to replace \( d \) with the expression you found in the first step.

4. **Conclusion**:
From the above steps, we conclude that the force experienced by the point charge \( q \) is proportional to:
\[ F \propto \frac{1}{(R + x)^2} \]

Therefore, the correct answer is that the force experienced by the point charge will be proportional to \( \frac{1}{(R + x)^2} \).

**Final Answer**: The correct option is **Option 3: \( \frac{1}{(R + x)^2} \)**.