Three charges are placed at the vertices of an equilateral triangle of side 10 cm. Assume `q_(1)=1 muC,q_(2)=-2 muC and q_(3)=4 muC`. Work done in separating the charges to infinity is

Options

A. `-4.5 J`
B. `4.5 J`
C. 45 J
D. None of these

Answer

To find the work done in separating the charges \( q_1 = 1 \, \mu C \), \( q_2 = -2 \, \mu C \), and \( q_3 = 4 \, \mu C \) placed at the vertices of an equilateral triangle with a side length of \( 10 \, cm \), we will calculate the potential energy of the system and then determine the work done in separating them to infinity.

### Step 1: Understand the potential energy formula
The potential energy \( U \) of a system of point charges is given by the formula:
\[
U = k \sum_{i