Two electric charges of `9mu C and -3mu C` are placed 0.16m apart in air. There are two points A and B on the line joining the two charges at distance of (1) 0.04m from `-3muC` and in between the charges and (ii) 0.08 m from `-3mu C` and out side the two charges. The potentials at A and B are

Options

A. 0V, 5V
B. 0V, 0V
C. 5V, 0V
D. 5V, 10V

Explanation

To find the electric potentials at points A and B due to the two charges \( Q_1 = 9 \, \mu C \) and \( Q_2 = -3 \, \mu C \), we can use the formula for electric potential \( V \) due to a point charge, which is given by:

\[ V = \frac{k \cdot Q}{r} \]

where:
- \( V \) is the electric potential,
- \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, N \cdot m^2/C^2 \)),
- \( Q \) is the charge,
- \( r \) is the distance from the charge to the point where the potential is being calculated.

### Step 1: Calculate the potential at point A

1. **Identify the distances**:
- The distance from \( -3 \, \mu C \) to point A is \( 0.04 \, m \).
- The distance from \( 9 \, \mu C \) to point A is \( 0.16 \, m - 0.04 \, m = 0.12 \, m \).

2. **Calculate the potential at A due to \( Q_1 \) (9 μC)**:
\[ V_{A1} = \frac{k \cdot Q_1}{r_{A1}} = \frac{8.99 \times 10^9 \cdot 9 \times 10^{-6}}{0.12} \]

3. **Calculate the potential at A due to \( Q_2 \) (-3 μC)**:
\[ V_{A2} = \frac{k \cdot Q_2}{r_{A2}} = \frac{8.99 \times 10^9 \cdot (-3) \times 10^{-6}}{0.04} \]

4. **Total potential at A**:
\[ V_A = V_{A1} + V_{A2} \]

### Step 2: Calculate the potential at point B

1. **Identify the distances**:
- The distance from \( -3 \, \mu C \) to point B is \( 0.08 \, m + 0.16 \, m = 0.24 \, m \).
- The distance from \( 9 \, \mu C \) to point B is \( 0.24 \, m - 0.16 \, m = 0.08 \, m \).

2. **Calculate the potential at B due to \( Q_1 \) (9 μC)**:
\[ V_{B1} = \frac{k \cdot Q_1}{r_{B1}} = \frac{8.99 \times 10^9 \cdot 9 \times 10^{-6}}{0.08} \]

3. **Calculate the potential at B due to \( Q_2 \) (-3 μC)**:
\[ V_{B2} = \frac{k \cdot Q_2}{r_{B2}} = \frac{8.99 \times 10^9 \cdot (-3) \times 10^{-6}}{0.24} \]

4. **Total potential at B**:
\[ V_B = V_{B1} + V_{B2} \]

### Final Calculation

Now we can plug in the values to calculate \( V_A \) and \( V_B \).