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` charge is

Options

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

Answer

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

### Step-by-Step Solution:

1. **Identify the Charges and Their Positions**:
- Let \( Q_1 = 12 \, \mu C \) (positive charge) and \( Q_2 = -6 \, \mu C \) (negative charge).
- The distance between the charges is \( d = 20 \, cm = 0.2 \, m \).

2. **Determine the Location of Point P**:
- Point P is located outside the region between the two charges. We will assume it is to the right of the -6 µC charge.

3. **Set Up the Equation for Electric Potential**:
- The electric potential \( V \) at point P due to charge \( Q_1 \) is given by:
\[ V_1 = \frac{k Q_1}{r_1} \]
- The electric potential \( V \) at point P due to charge \( Q_2 \) is given by:
\[ V_2 = \frac{k Q_2}{r_2} \]
- The total potential at point P is:
\[ V = V_1 + V_2 = 0 \]

4. **Express the Distances**:
- Let \( x \) be the distance from point P to the charge \( Q_2 \) (-6 µC).
- Therefore, the distance from point P to charge \( Q_1 \) (12 µC) is \( r_1 = 20 \, cm + x = 0.2 + x \).

5. **Set Up the Equation**:
- Since \( V = 0 \), we have:
\[ \frac{k Q_1}{r_1} + \frac{k Q_2}{r_2} = 0 \]
- Substituting the values:
\[ \frac{12 \times 10^{-6}}{0.2 + x} + \frac{-6 \times 10^{-6}}{x} = 0 \]
- Simplifying gives:
\[ \frac{12}{0.2 + x} = \frac{6}{x} \]

6. **Cross Multiply**:
- Cross multiplying gives:
\[ 12x = 6(0.2 + x) \]
- Expanding the right side:
\[ 12x = 1.2 + 6x \]

7. **Solve for x**:
- Rearranging gives:
\[ 12x - 6x = 1.2 \]
- Thus:
\[ 6x = 1.2 \implies x = \frac{1.2}{6} = 0.2 \, m = 20 \, cm \]

8. **Conclusion**:
- The distance of point P from the -6 µC charge is \( 20 \, cm \).

### Final Answer:
The distance of point P from the -6 µC charge is **20 cm**.