8) Three charges \(2q\), \(-q\), and \(-q\) are located at the vertices of an equilateral triangle. What is the net field and potential at the centre of the triangle?
Solution:
The electric potential at a point due to a point charge is a scalar quantity. For the three charges, the total potential at the centre is given by: \[ V = k\left(\frac{2q}{R} - \frac{q}{R} - \frac{q}{R}\right) = 0, \] where \(R\) is the distance from the centre to each vertex. Thus, the net potential is zero.
The electric field, however, is a vector quantity. Even though the algebraic sum of the charges is zero, their vector contributions do not cancel completely due to their directions. In this configuration, the field contributions from the two \(-q\) charges combine and do not exactly cancel the field due to \(2q\). Hence, the net electric field at the centre is non-zero.
Therefore, the correct answer is option B: The field is non-zero but potential is zero.
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