The net electric force on a charge of `+3 muC` at the mid-point on the line joining two charges of magnitude `+2 muC` and `+2 muC` separated by the distance of 6 mm, is

Options

A. 6000 N
B. 500 N
C. 60 N
D. zero

Answer

To solve the problem of finding the net electric force on a charge of \( +3 \mu C \) at the midpoint between two charges of \( +2 \mu C \) each, separated by a distance of 6 mm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Charges and Their Positions**:
- Let \( Q_1 = +2 \mu C \) be at position \( A \) (0 mm).
- Let \( Q_2 = +2 \mu C \) be at position \( B \) (6 mm).
- The charge \( Q = +3 \mu C \) is placed at the midpoint \( M \) (3 mm).

2. **Calculate the Distance from the Midpoint to Each Charge**:
- The distance from the midpoint \( M \) to each charge \( Q_1 \) and \( Q_2 \) is:
\[ R = \frac{6 \text{ mm}}{2} = 3 \text{ mm} = 0.003 \text{ m} \]

3. **Calculate the Electric Field Due to Each Charge at the Midpoint**:
- The electric field \( E \) due to a point charge is given by:
\[ E = \frac{1}{4 \pi \epsilon_0} \frac{Q}{R^2} \]
- For \( Q_1 \):
\[ E_1 = \frac{1}{4 \pi \epsilon_0} \frac{2 \times 10^{-6}}{(0.003)^2} \]
- For \( Q_2 \):
\[ E_2 = \frac{1}{4 \pi \epsilon_0} \frac{2 \times 10^{-6}}{(0.003)^2} \]

4. **Direction of the Electric Fields**:
- Both \( E_1 \) and \( E_2 \) will point away from the charges since they are positive.
- Therefore, at point \( M \):
- \( E_1 \) points to the right (away from \( Q_1 \)).
- \( E_2 \) points to the left (away from \( Q_2 \)).

5. **Calculate the Net Electric Field at the Midpoint**:
- Since both electric fields are equal in magnitude but opposite in direction:
\[ E_{\text{net}} = E_1 - E_2 = 0 \]

6. **Calculate the Net Electric Force on the Charge at the Midpoint**:
- The force \( F \) on the charge \( Q \) is given by:
\[ F = Q \cdot E_{\text{net}} \]
- Substituting \( E_{\text{net}} = 0 \):
\[ F = 3 \times 10^{-6} \cdot 0 = 0 \]

### Conclusion:
The net electric force on the charge of \( +3 \mu C \) at the midpoint is \( 0 \, N \).