Two charges of 10 C and - 15 C are separated in air by 1m. The ratio of force exerted by one on the other is

Options

A. `1:2`
B. `2:1`
C. `1:1`
D. None of these

Explanation

To solve the problem of finding the ratio of the forces exerted by two charges on each other, we can follow these steps:

### Step 1: Identify the Charges and Distance
We have two charges:
- Charge \( Q_1 = 10 \, C \) (positive)
- Charge \( Q_2 = -15 \, C \) (negative)

The distance \( R \) between the charges is given as \( 1 \, m \).

### Step 2: Apply Coulomb's Law
Coulomb's Law states that the force \( F \) between two point charges is given by the formula:
\[ F = k \frac{|Q_1 Q_2|}{R^2} \]
where \( k \) is Coulomb's constant, approximately \( 8.99 \times 10^9 \, N \cdot m^2/C^2 \).

### Step 3: Calculate the Forces
Using Coulomb's Law, we can calculate the force exerted by \( Q_1 \) on \( Q_2 \) (denoted as \( F_{12} \)) and the force exerted by \( Q_2 \) on \( Q_1 \) (denoted as \( F_{21} \)):
\[ F_{12} = k \frac{|Q_1 Q_2|}{R^2} = k \frac{|10 \times (-15)|}{1^2} = k \frac{150}{1} = 150k \]
\[ F_{21} = k \frac{|Q_2 Q_1|}{R^2} = k \frac{|-15 \times 10|}{1^2} = k \frac{150}{1} = 150k \]

### Step 4: Determine the Ratio of Forces
According to Newton's Third Law, the forces exerted by the charges on each other are equal in magnitude and opposite in direction:
\[ F_{12} = F_{21} \]
Thus, the ratio of the forces is:
\[ \frac{F_{12}}{F_{21}} = \frac{150k}{150k} = 1 \]

### Conclusion
The ratio of the force exerted by one charge on the other is:
\[ \text{Ratio} = 1 : 1 \]

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