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Scaling every linear dimension of a parallel plate capacitor by a factor \( k \) changes its capacitance by

  • A.\( k^2 \)
  • B.\( k^3 \)
  • C.unity
  • D.\( k \)

Answer: D

The area grows as \( k^2 \) and the separation as \( k \), so the ratio grows as the first power of the scale. Capacitance therefore has the dimensions of a permittivity times a length, which is the same conclusion the isolated sphere formula reaches.

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