There are two charges `+1 mu C ` and`-5 mu C` under mutual coulombic interaction . The ratio of magnitude of forces acting on themwill be `

Options

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

Answer

To solve the problem of finding the ratio of the magnitudes of the forces acting on two charges \(+1 \, \mu C\) and \(-5 \, \mu C\) under mutual Coulombic interaction, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Charges**:
Let \(q_1 = +1 \, \mu C = 1 \times 10^{-6} \, C\) and \(q_2 = -5 \, \mu C = -5 \times 10^{-6} \, C\).

2. **Coulomb's Law**:
According to Coulomb's law, the magnitude of the force \(F\) between two point charges is given by the formula:
\[ F = k \frac{|q_1 q_2|}{d^2} \]
where \(k\) is Coulomb's constant (approximately \(8.99 \times 10^9 \, N m^2/C^2\)) and \(d\) is the distance between the charges.

3. **Calculate the Forces**:
The force on \(q_1\) due to \(q_2\) is \(F_{12}\) and the force on \(q_2\) due to \(q_1\) is \(F_{21}\). According to Newton's third law, these forces are equal in magnitude but opposite in direction:
\[ F_{12} = k \frac{|q_1 q_2|}{d^2} \quad \text{and} \quad F_{21} = k \frac{|q_1 q_2|}{d^2} \]

4. **Ratio of Forces**:
Since \(F_{12}\) and \(F_{21}\) are equal in magnitude:
\[ |F_{12}| = |F_{21}| \]
Therefore, the ratio of the magnitudes of the forces acting on the two charges is:
\[ \frac{|F_{12}|}{|F_{21}|} = 1 \]

5. **Conclusion**:
The ratio of the magnitudes of the forces acting on the charges \(+1 \, \mu C\) and \(-5 \, \mu C\) is \(1:1\).

### Final Answer:
The ratio of the magnitude of forces acting on the charges is \(1:1\).

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