A charge of 0.5 nC is placed at the centre of an equilateral triangle of side 10 cm, calculate the work done in bringing a charge of 0.1 nC from infinity to any vertices of the triangle.

Explanation

To solve the problem of calculating the work done in bringing a charge of 0.1 nC from infinity to any vertex of an equilateral triangle with a charge of 0.5 nC at its center, we can follow these steps:

### Step 1: Understand the Configuration
We have an equilateral triangle with a side length of 10 cm. A charge \( q_1 = 0.5 \, \text{nC} \) is placed at the center of the triangle. We need to bring another charge \( q_2 = 0.1 \, \text{nC} \) from infinity to one of the vertices of the triangle.

### Step 2: Calculate the Distance from the Center to a Vertex
For an equilateral triangle, the distance from the center to a vertex can be calculated using the formula:
\[
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