Two charges repel each other with a force of 200N. One of the charges is increased by 20% and otht is reduced by 10%. The new repulsive force at same distance would be

Options

A. 200N
B. 216N
C. 300N
D. 316N

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the initial conditions
We know that the initial repulsive force \( F \) between two charges \( Q_1 \) and \( Q_2 \) is given as:
\[ F = 200 \, \text{N} \]

### Step 2: Identify the changes in charges
One charge is increased by 20%, and the other is decreased by 10%. We can express the new charges as follows:
- The new charge \( Q_1' \) after a 20% increase:
\[ Q_1' = Q_1 + 0.2Q_1 = 1.2Q_1 \]
- The new charge \( Q_2' \) after a 10% decrease:
\[ Q_2' = Q_2 - 0.1Q_2 = 0.9Q_2 \]

### Step 3: Write the formula for the new force
According to Coulomb's law, the force \( F' \) between the new charges at the same distance \( r \) is given by:
\[ F' = \frac{1}{4\pi \epsilon_0} \frac{Q_1' Q_2'}{r^2} \]

Substituting the new charges into the equation:
\[ F' = \frac{1}{4\pi \epsilon_0} \frac{(1.2Q_1)(0.9Q_2)}{r^2} \]

### Step 4: Relate the new force to the initial force
We can express the new force \( F' \) in terms of the initial force \( F \):
\[ F' = \frac{1.2 \cdot 0.9}{1} \cdot F \]
Calculating \( 1.2 \cdot 0.9 \):
\[ 1.2 \cdot 0.9 = 1.08 \]
Thus, we can write:
\[ F' = 1.08 \cdot F \]

### Step 5: Calculate the new force
Now substituting the value of \( F \):
\[ F' = 1.08 \cdot 200 \, \text{N} = 216 \, \text{N} \]

### Conclusion
The new repulsive force at the same distance after the changes in the charges is:
\[ \boxed{216 \, \text{N}} \]