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 solve the problem of finding the intensity of the electric field at the vertex of a regular tetrahedron, where the base is an equilateral triangle formed by three identical positive charges \( Q \), 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 with side length \( a \). We need to find the electric field at the vertex of a tetrahedron that is directly above the center of this triangle.

### Step 2: Find the Position of the Charges
Let the charges be located at points \( A \), \( B \), and \( C \) of the triangle. The centroid \( G \) of the triangle can be calculated as:
\[
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