Two electric charges `12 mu C` and `-6 mu C` are placed `20 cm` apart in air. There will be a point `P` on the line joining these charges and outside the region between them, at which the electric potential is zero. The distance of `P` from `6 mu C` chrage is

Options

A. `0.10 m`
B. `0.15 m`
C. `0.20 m`
D. `0.25 m`

Explanation

To find the distance of point P from the -6 µC charge where the electric potential is zero, we can follow these steps:

### Step 1: Understand the Setup
We have two charges:
- Charge \( Q_1 = 12 \, \mu C = 12 \times 10^{-6} \, C \)
- Charge \( Q_2 = -6 \, \mu C = -6 \times 10^{-6} \, C \)

The distance between the two charges is \( d = 20 \, cm = 0.2 \, m \).

### Step 2: Define the Position of Point P
Let the distance from the -6 µC charge to point P be \( x \). Since point P is outside the region between the charges, the distance from the 12 µC charge to point P will be \( (0.2 + x) \).

### Step 3: Write the Expression for Electric Potential
The electric potential \( V \) at point P due to both charges is given by the formula:
\[ V = k \left( \frac{Q_1}{r_1} + \frac{Q_2}{r_2} \right) \]
where:
- \( k \) is the electrostatic constant \( (8.99 \times 10^9 \, N m^2/C^2) \)
- \( r_1 \) is the distance from \( Q_1 \) to point P, which is \( (0.2 + x) \)
- \( r_2 \) is the distance from \( Q_2 \) to point P, which is \( x \)

Thus, we have:
\[ V = k \left( \frac{12 \times 10^{-6}}{0.2 + x} + \frac{-6 \times 10^{-6}}{x} \right) \]

### Step 4: Set the Electric Potential to Zero
To find the point where the electric potential is zero, we set the equation to zero:
\[ \frac{12 \times 10^{-6}}{0.2 + x} - \frac{6 \times 10^{-6}}{x} = 0 \]

### Step 5: Solve for x
Rearranging the equation gives:
\[ \frac{12}{0.2 + x} = \frac{6}{x} \]
Cross-multiplying:
\[ 12x = 6(0.2 + x) \]
Expanding:
\[ 12x = 1.2 + 6x \]
Rearranging gives:
\[ 12x - 6x = 1.2 \]
\[ 6x = 1.2 \]
Dividing both sides by 6:
\[ x = 0.2 \, m \]

### Step 6: Conclusion
The distance of point P from the -6 µC charge is \( 0.2 \, m \) or \( 20 \, cm \).