Three identical positive charges Q are arranged at the vertices of an equilateral triangle. The side of the triangle is a. Find the intensity of the field at the vertex of a regular tetrahedron of which the triangle is the base.

Explanation

To find the intensity of the electric field at the vertex of a regular tetrahedron formed by three identical positive charges \( Q \) arranged at the vertices of an equilateral triangle with side length \( a \), we can follow these steps:

### Step 1: Understand the Configuration
We have three identical positive charges \( Q \) located at the vertices of an equilateral triangle. The fourth vertex of the tetrahedron is directly above the centroid of this triangle.

### Step 2: Calculate the Electric Field Due to One Charge
The electric field \( E \) due to a single charge \( Q \) at a distance \( r \) is given by:
\[
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