Two charges each equal to `2mu C` are o.5 m apart. If both of them exist inside vacuum, then the force between them is

Options

A. 1.89 N
B. 2.44 N
C. 0.144 N
D. 3.144 N

Answer

To find the force between two charges using Coulomb's law, we can follow these steps:

### Step 1: Identify the given values
- Charge \( q_1 = 2 \, \mu C = 2 \times 10^{-6} \, C \)
- Charge \( q_2 = 2 \, \mu C = 2 \times 10^{-6} \, C \)
- Distance \( R = 0.5 \, m \)

### Step 2: Write down Coulomb's law
Coulomb's law states that the force \( F \) between two point charges is given by the formula:
\[ F = \frac{k \cdot |q_1 \cdot q_2|}{R^2} \]
where \( k \) is Coulomb's constant, approximately \( 9 \times 10^9 \, N \cdot m^2/C^2 \).

### Step 3: Substitute the values into the formula
Substituting the known values into the equation:
\[ F = \frac{9 \times 10^9 \cdot |2 \times 10^{-6} \cdot 2 \times 10^{-6}|}{(0.5)^2} \]

### Step 4: Calculate the numerator
First, calculate the product of the charges:
\[ |q_1 \cdot q_2| = 2 \times 10^{-6} \cdot 2 \times 10^{-6} = 4 \times 10^{-12} \, C^2 \]
Now substitute this back into the formula:
\[ F = \frac{9 \times 10^9 \cdot 4 \times 10^{-12}}{(0.5)^2} \]

### Step 5: Calculate the denominator
Calculate \( (0.5)^2 \):
\[ (0.5)^2 = 0.25 \]

### Step 6: Substitute the denominator back into the equation
Now substitute back into the force equation:
\[ F = \frac{9 \times 10^9 \cdot 4 \times 10^{-12}}{0.25} \]

### Step 7: Simplify the equation
Calculating the division:
\[ F = 9 \times 10^9 \cdot 4 \times 10^{-12} \cdot 4 = 36 \times 10^{-3} = 0.144 \, N \]

### Step 8: Final result
Thus, the force between the two charges is:
\[ F = 0.144 \, N \]