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Comparing the ease of computing the field and the potential of an awkward charge distribution, the potential is easier because

  • A.it can be computed without knowing where the charges lie
  • B.it is a scalar and needs no resolution into components
  • C.its integral converges where that for the field does not
  • D.it does not require the permittivity of the medium

Answer: B

Correct answer: it is a scalar and needs no resolution into components

The potential of a distribution is a single integral of a scalar, whereas the field requires the vector contributions to be resolved and integrated component by component. The usual practice is therefore to compute the potential and then take its gradient, which is far less work than integrating the field directly.

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