Two point charges repel each other with a force of 100N. One of the charges is increased by 10% and the other is reduced by 10% . The new force of repulsion at the same distance would be

Options

A. 100N
B. 121N
C. 99N
D. none of these

Explanation

To solve the problem step by step, we will use Coulomb's Law, which states that the electrostatic force \( F \) between two point charges \( Q_1 \) and \( Q_2 \) separated by a distance \( r \) is given by:

\[ F = \frac{k \cdot Q_1 \cdot Q_2}{r^2} \]

where \( k \) is Coulomb's constant.

### Step 1: Understand the initial conditions
Initially, we have two charges \( Q \) and \( Q \) (both are the same charge), and the force of repulsion between them is given as \( F = 100 \, \text{N} \).

### Step 2: Express the initial force
Using Coulomb's Law:

\[ F = \frac{k \cdot Q \cdot Q}{r^2} = 100 \, \text{N} \]

This can be simplified to:

\[ F = \frac{k \cdot Q^2}{r^2} \quad \text{(Equation 1)} \]

### Step 3: Modify the charges
According to the problem, one charge is increased by 10%, and the other is decreased by 10%.

- The new charge after increasing by 10%:
\[ Q_1 = 1.1Q \]

- The new charge after decreasing by 10%:
\[ Q_2 = 0.9Q \]

### Step 4: Calculate the new force
Now, we need to calculate the new force \( F' \) with the new charges \( Q_1 \) and \( Q_2 \):

\[ F' = \frac{k \cdot Q_1 \cdot Q_2}{r^2} = \frac{k \cdot (1.1Q) \cdot (0.9Q)}{r^2} \]

### Step 5: Substitute the values
Substituting the values of \( Q_1 \) and \( Q_2 \):

\[ F' = \frac{k \cdot (1.1Q) \cdot (0.9Q)}{r^2} = \frac{k \cdot Q^2 \cdot (1.1 \cdot 0.9)}{r^2} \]

### Step 6: Simplify using the initial force
From Equation 1, we know:

\[ \frac{k \cdot Q^2}{r^2} = 100 \, \text{N} \]

Thus, we can substitute this into our equation for \( F' \):

\[ F' = 100 \cdot (1.1 \cdot 0.9) \]

### Step 7: Calculate \( 1.1 \cdot 0.9 \)
Calculating \( 1.1 \cdot 0.9 \):

\[ 1.1 \cdot 0.9 = 0.99 \]

### Step 8: Final calculation of the new force
Now, substituting this back into the equation for \( F' \):

\[ F' = 100 \cdot 0.99 = 99 \, \text{N} \]

### Conclusion
The new force of repulsion between the two charges after the changes is:

\[ \boxed{99 \, \text{N}} \]

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