There are two charge `+1mu c` and `+2muc` kept at certain separation ,the ratio of electrostatic forces acting on them will be in the ratio

Options

A. `1 : 5`
B. `1 : 1`
C. `5 : 1`
D. `1 : 25`

Answer

To find the ratio of the electrostatic forces acting on two charges \( Q_1 \) and \( Q_2 \), we can use Coulomb's law, which states that the force \( F \) between two point charges is given by:

\[ F = k \frac{|Q_1 Q_2|}{R^2} \]

where:
- \( F \) is the magnitude of the electrostatic force,
- \( k \) is Coulomb's constant,
- \( Q_1 \) and \( Q_2 \) are the magnitudes of the charges,
- \( R \) is the separation between the charges.

### Step 1: Identify the charges
Given:
- \( Q_1 = +1 \, \mu C = 1 \times 10^{-6} \, C \)
- \( Q_2 = +2 \, \mu C = 2 \times 10^{-6} \, C \)

### Step 2: Write the expression for the forces
According to Coulomb's law, the force on charge \( Q_1 \) due to \( Q_2 \) (denoted as \( F_{12} \)) and the force on charge \( Q_2 \) due to \( Q_1 \) (denoted as \( F_{21} \)) can be expressed as:

\[ F_{12} = k \frac{|Q_1 Q_2|}{R^2} \]
\[ F_{21} = k \frac{|Q_2 Q_1|}{R^2} \]

### Step 3: Calculate the forces
Since \( F_{12} \) and \( F_{21} \) are equal in magnitude (by Newton's third law), we can write:

\[ F_{12} = F_{21} \]

### Step 4: Ratio of the forces
Now, we can find the ratio of the forces acting on the charges:

\[ \text{Ratio} = \frac{F_{12}}{F_{21}} = \frac{k \frac{|Q_1 Q_2|}{R^2}}{k \frac{|Q_2 Q_1|}{R^2}} = \frac{|Q_1 Q_2|}{|Q_2 Q_1|} = 1 \]

### Conclusion
Thus, the ratio of the electrostatic forces acting on the two charges is:

\[ \text{Ratio} = 1 : 1 \]

### Final Answer
The ratio of the electrostatic forces acting on the charges \( +1 \, \mu C \) and \( +2 \, \mu C \) is \( 1 : 1 \).

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