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The potential at the centre of a square of side \( a \) with equal charges \( Q \) at each corner is

  • A.\( 4Q/(4\pi\epsilon_0 \cdot a/\sqrt{2}) \)
  • B.zero
  • C.\( Q/(4\pi\epsilon_0 a) \)
  • D.\( 4Q/(4\pi\epsilon_0 a) \)

Answer: A

Each corner is at a distance of half the diagonal, that is \( a/\sqrt{2} \), and being scalars the four contributions simply add. The field at the same point, by contrast, is exactly zero, since the four vector contributions cancel in opposite pairs, which is a good illustration of how differently the two quantities behave.

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