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A charge Q produces an electric field described by E = k|Q|/r^2. At a distance of 2 cm from the charge, how does the field strength compare with the field strength at 4 cm from the same charge?

AIt is four times stronger at 2 cm than at 4 cm
BIt is two times stronger at 2 cm than at 4 cm
CIt is the same strength at both distances
DIt is four times weaker at 2 cm than at 4 cm
Answer & Solution
Correct answer: A. It is four times stronger at 2 cm than at 4 cm
1. The field from a point charge falls off as 1/r^2. 2. Halving the distance from 4 cm to 2 cm multiplies the field by (4/2)^2 = 4. 3. So the field at 2 cm is four times stronger than the field at 4 cm. 4. Assuming the field only doubles, as in option B, mistakes an inverse-square relationship for a simple inverse relationship. _Source: OpenStax Physics (CC BY 4.0), Ch 18 "Static Electricity", section 18.3 Electric Field_
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