There are two charges +1 microcoulombs and +5 microcoulombs. The ratio of the forces acting on them will 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 forces acting on two charges, we can follow these steps:

### Step-by-Step Solution:

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

2. **Understand the Nature of Forces**:
Since both charges are positive, the forces acting on each other will be repulsive.

3. **Use Coulomb's Law**:
According to Coulomb's Law, the force \( F \) between two point charges is given by:
\[ F = k \frac{|q_1 q_2|}{r^2} \]
where \( k \) is Coulomb's constant, and \( r \) is the distance between the charges.

4. **Calculate the Force on Each Charge**:
- The force on \( q_1 \) due to \( q_2 \) is:
\[ F_{q_1} = k \frac{|q_1 q_2|}{r^2} = k \frac{(1 \times 10^{-6})(5 \times 10^{-6})}{r^2} \]
- The force on \( q_2 \) due to \( q_1 \) is:
\[ F_{q_2} = k \frac{|q_1 q_2|}{r^2} = k \frac{(1 \times 10^{-6})(5 \times 10^{-6})}{r^2} \]

5. **Find the Ratio of the Forces**:
The ratio of the forces acting on the two charges is:
\[ \frac{F_{q_1}}{F_{q_2}} = \frac{k \frac{|q_1 q_2|}{r^2}}{k \frac{|q_1 q_2|}{r^2}} = 1 \]
Therefore, the ratio of the forces is:
\[ F_{q_1} : F_{q_2} = 1 : 1 \]

6. **Conclusion**:
The ratio of the forces acting on the two charges is \( 1 : 1 \).