Potential at a point 0.1m 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 negative

Answer

To determine the nature of the point charge based on the given potential at a distance from it, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Electric Potential (V)**:
The electric potential (V) due to a point charge (Q) at a distance (r) from it is given by the formula:
\[ V = \frac{1}{4 \pi \epsilon_0} \cdot \frac{Q}{r} \]
where \(\epsilon_0\) is the permittivity of free space.

2. **Given Values**:
We are given:
- Distance \(r = 0.1 \, m\)
- Electric potential \(V = +100 \, V\)

3. **Rearranging the Formula**:
We can rearrange the formula to find the charge \(Q\):
\[ Q = V \cdot 4 \pi \epsilon_0 \cdot r \]

4. **Substituting the Values**:
We substitute the known values into the equation. The value of \(\epsilon_0\) is approximately \(8.85 \times 10^{-12} \, C^2/(N \cdot m^2)\):
\[ Q = 100 \cdot 4 \pi (8.85 \times 10^{-12}) \cdot 0.1 \]

5. **Calculating Q**:
First, calculate \(4 \pi \epsilon_0\):
\[ 4 \pi (8.85 \times 10^{-12}) \approx 1.112 \times 10^{-10} \, C^2/(N \cdot m^2) \]
Now substituting this back into the equation for \(Q\):
\[ Q = 100 \cdot (1.112 \times 10^{-10}) \cdot 0.1 = 1.112 \times 10^{-11} \, C \]

6. **Determining the Nature of the Charge**:
Since the potential \(V\) at the point is positive (+100 V), it indicates that the charge \(Q\) must also be positive. This is because the potential due to a positive charge is positive, while the potential due to a negative charge would be negative.

7. **Conclusion**:
Therefore, the nature of the point charge is **positive**.