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(D) Equipotential surfaces represent regions where the electric potential is constant. For a system of three equal charges placed at the vertices of a

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$d$

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(D) Equipotential surfaces represent regions where the electric potential is constant. For a system of three equal charges placed at the vertices of an equilateral triangle,the symmetry of the charge distribution must be reflected in the equipotential lines.$1$. Near each individual charge,the equipotential surfaces are approximately circular,as the potential is dominated by the nearest charge.$2$. As we move further away from the charges,the individual equipotential surfaces merge due to the superposition of the potentials from all three charges.$3$. Because the charges are equal and arranged in an equilateral triangle,the resulting equipotential pattern must exhibit $C_3$ rotational symmetry about the centroid of the triangle.$4$. Graph $(d)$ is the only one that shows this threefold symmetry,where the equipotential lines surround all three charges collectively at larger distances while maintaining distinct circular patterns near each charge.Therefore,graph $(d)$ is the correct representation.

Three equal charges are placed at the corners of an equilateral triangle. Which of the graphs below correctly depicts the equally-spaced equipotential surfaces in the plane of the triangle? (All graphs have the same scale.)

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