Two similar and equal charges repel each other with force of 1.6 N. When placed 3m apart Strength of each charge is -

Options

A. `40 mu C`
B. `20 mu C`
C. `4 mu C`
D. `2 mu C`

Answer

To solve the problem, we will use Coulomb's law, which states that the force \( F \) between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) is given by:

\[ F = k \frac{q_1 q_2}{r^2} \]

where \( k \) is Coulomb's constant, approximately \( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \).

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Force \( F = 1.6 \, \text{N} \)
- Distance \( r = 3 \, \text{m} \)
- Since the charges are equal, let \( q_1 = q_2 = q \).

2. **Substitute Values into Coulomb's Law**:
\[ F = k \frac{q^2}{r^2} \]
Substituting the known values:
\[ 1.6 = 9 \times 10^9 \frac{q^2}{(3)^2} \]

3. **Calculate \( r^2 \)**:
\[ r^2 = 3^2 = 9 \]

4. **Rearrange the Equation**:
\[ 1.6 = 9 \times 10^9 \frac{q^2}{9} \]
Simplifying gives:
\[ 1.6 = 10^9 q^2 \]

5. **Solve for \( q^2 \)**:
\[ q^2 = \frac{1.6}{10^9} \]
\[ q^2 = 1.6 \times 10^{-9} \]

6. **Take the Square Root to Find \( q \)**:
\[ q = \sqrt{1.6 \times 10^{-9}} \]
Breaking it down:
\[ q = \sqrt{16 \times 10^{-10}} = 4 \times 10^{-5} \]

7. **Convert to Microcoulombs**:
\[ q = 4 \times 10^{-5} \, \text{C} = 40 \, \mu\text{C} \]

### Final Answer:
The strength of each charge is \( 40 \, \mu\text{C} \).

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