There are two charges +1 `muC` and `+5muC`, separated by a distance of 0.2 m in air, the ratio of forces acting in them will be:

Options

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

Answer

To solve the problem of finding the ratio of forces acting on two charges \( +1 \mu C \) and \( +5 \mu C \) separated by a distance of \( 0.2 \, m \), we can use Coulomb's Law. Here’s the step-by-step solution:

### Step 1: Identify the charges and distance
We have two charges:
- \( q_1 = +1 \mu C = 1 \times 10^{-6} C \)
- \( q_2 = +5 \mu C = 5 \times 10^{-6} C \)

The distance between them is:
- \( r = 0.2 \, m \)

### Step 2: Write down Coulomb's Law
Coulomb's Law states that 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, approximately \( 8.99 \times 10^9 \, N m^2/C^2 \).

### Step 3: Calculate the force acting on charge \( q_1 \) due to \( q_2 \)
Using Coulomb's Law, the force \( F_{12} \) acting on \( q_1 \) due to \( q_2 \) is:
\[ F_{12} = k \frac{|q_1 q_2|}{r^2} \]
Substituting the values:
\[ F_{12} = 8.99 \times 10^9 \frac{|(1 \times 10^{-6})(5 \times 10^{-6})|}{(0.2)^2} \]
Calculating the denominator:
\[ (0.2)^2 = 0.04 \]
Now substituting back:
\[ F_{12} = 8.99 \times 10^9 \frac{5 \times 10^{-12}}{0.04} \]
Calculating:
\[ F_{12} = 8.99 \times 10^9 \times 1.25 \times 10^{-10} = 1.12375 \, N \]

### Step 4: Calculate the force acting on charge \( q_2 \) due to \( q_1 \)
By symmetry, the force \( F_{21} \) acting on \( q_2 \) due to \( q_1 \) is given by the same formula:
\[ F_{21} = k \frac{|q_1 q_2|}{r^2} \]
Since \( q_1 \) and \( q_2 \) are the same charges, the calculation will yield the same force:
\[ F_{21} = 1.12375 \, N \]

### Step 5: Find the ratio of forces
Now, we find the ratio of the forces:
\[ \text{Ratio} = \frac{F_{12}}{F_{21}} = \frac{1.12375}{1.12375} = 1 \]

### Final Answer
The ratio of forces acting on the two charges is:
\[ \text{Ratio} = 1:1 \]