The potential at a point 0.1 m from an isolated point charge is + 100 volt. The nature of the point charge is

Options

A. positive
B. negative
C. zero
D. either positive or zero

Answer

To determine the nature of the point charge based on the given potential, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Distance from the point charge, \( R = 0.1 \, \text{m} \)
- Electric potential at that distance, \( V = +100 \, \text{V} \)

2. **Use the Formula for Electric Potential**:
The electric potential \( V \) due to a point charge \( Q \) at a distance \( R \) is given by the formula:
\[ V = \frac{kQ}{R} \]
where \( k \) is Coulomb's constant (approximately \( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)).

3. **Rearranging the Formula**:
We can rearrange the formula to solve for \( Q \):
\[ Q = \frac{VR}{k} \]

4. **Substituting the Values**:
Substitute the known values into the equation:
\[ Q = \frac{(100 \, \text{V})(0.1 \, \text{m})}{k} \]
Since \( k \) is a positive constant, the sign of \( Q \) will depend on the sign of \( V \).

5. **Analyzing the Sign**:
Given that \( V = +100 \, \text{V} \) is positive, and since \( k \) and \( R \) are also positive, it follows that:
- For \( V \) to be positive, \( Q \) must also be positive (because a positive \( Q \) creates a positive potential).

6. **Conclusion**:
Therefore, the nature of the point charge \( Q \) is **positive**.

### Final Answer:
The nature of the point charge is **positive**.

---