Physics

Problem

Three point charges occupy the corners of an equilateral triangle of side 0.25 m:

q_1 = +3.0\,\mu\text{C}

(top),

q_2 = -2.0\,\mu\text{C}

(lower left), and

q_3 = +4.0\,\mu\text{C}

(lower right). A fourth charge

q_4 = +1.5\,\mu\text{C}

is brought from infinitely far away to the center of the triangle. Determine the magnitude of the external work required to place

q_4

at the center.

Intuitive explanation

The key is recognizing that external work equals the change in electric potential energy of the system—specifically, the work needed to bring $q_4$ against the electric potential created by the three fixed charges. Rather than calculating forces directly, find the electric potential at the triangle's center due to $q_1$ , $q_2$ , and $q_3$ , then multiply by $q_4$ to get the potential energy change. The symmetry of the equilateral triangle makes the geometry straightforward once you identify that all three charges are equidistant from the center.

Intuitive explanation

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