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 at a distance from it, we can follow these steps:

### Step 1: Understand the relationship between potential and charge
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 \( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \).

### Step 2: Plug in the known values
We know:
- The potential \( V = +100 \, \text{V} \)
- The distance \( R = 0.1 \, \text{m} \)
- The value of \( k = 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \)

Substituting these values into the formula:
\[ 100 = \frac{9 \times 10^9 \cdot Q}{0.1} \]

### Step 3: Solve for \( Q \)
Rearranging the equation to solve for \( Q \):
\[ Q = \frac{100 \cdot 0.1}{9 \times 10^9} \]
\[ Q = \frac{10}{9 \times 10^9} \]
\[ Q = 1.11 \times 10^{-9} \, \text{C} \]

### Step 4: Determine the nature of the charge
Since the potential \( V \) at the point is positive (+100 V), and we have calculated \( Q \) to be positive, we can conclude that the nature of the point charge is positive.

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

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