My Math Forum Force of Attraction between ions

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 March 12th, 2016, 05:03 PM #1 Senior Member     Joined: Nov 2015 From: Alabama Posts: 114 Thanks: 15 Math Focus: Trigonometry, Calculus, Physics Force of Attraction between ions I got a very interesting questions on my mock general chemistry exam on Friday. It says "If you double the distance between two ions the force of attraction between them is multiplied by what?" I went with 2. The correct answer is 1/4. I would love to know why I am totally wrong? I would think the two ions would be trying harder to stay together, and therefore the force would double. But 1/4 does not make any sense to me. Thanks!
 March 12th, 2016, 07:40 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,579 Thanks: 1275 Elecctrostatic force follows the inverse square law, it is inversely proportional to the square of the distance between the two charges. $F \, \alpha \, \dfrac{1}{d^2}$ double the distance, $d$ ... $\dfrac{1}{(2d)^2} = \dfrac{1}{4d^2} = \dfrac{1}{4} \cdot \dfrac{1}{d^2} \, \alpha \, \dfrac{1}{4} \cdot F$ Thanks from SenatorArmstrong
March 12th, 2016, 07:47 PM   #3
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Quote:
 Originally Posted by skeeter Elecctrostatic force follows the inverse square law, it is inversely proportional to the square of the distance between the two charges. $F \, \alpha \, \dfrac{1}{d^2}$ double the distance, $d$ ... $\dfrac{1}{(2d)^2} = \dfrac{1}{4d^2} = \dfrac{1}{4} \cdot \dfrac{1}{d^2} \, \alpha \, \dfrac{1}{4} \cdot F$
Thank you so much!

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