If the distance in Coulomb’s law is doubled, by what factor does the electric field E = kq/r^2 change?

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Study for the UCF PHY2054 General Physics Exam. Use flashcards and multiple-choice questions complete with hints and explanations. Boost your understanding and get exam-ready!

Multiple Choice

If the distance in Coulomb’s law is doubled, by what factor does the electric field E = kq/r^2 change?

Explanation:
Electric field from a point charge scales as E = k q / r^2, so it is inversely proportional to the square of the distance. If the distance is doubled, r becomes 2r, and E becomes k q / (2r)^2 = k q / (4 r^2) = (1/4) times the original E. In other words, the field is reduced by a factor of 4, or becomes one quarter of its initial value.

Electric field from a point charge scales as E = k q / r^2, so it is inversely proportional to the square of the distance. If the distance is doubled, r becomes 2r, and E becomes k q / (2r)^2 = k q / (4 r^2) = (1/4) times the original E. In other words, the field is reduced by a factor of 4, or becomes one quarter of its initial value.

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