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The force between a 40 "mu"C charge and a  -50 "mu"C charge is 2.3 N.  How far apart...

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lkehoe | Valedictorian

Posted May 13, 2013 at 4:45 PM via web

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The force between a 40 "mu"C charge and a  -50 "mu"C charge is 2.3 N.  How far apart are they?`mu`

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted May 13, 2013 at 6:34 PM (Answer #1)

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You need to use Coulomb's law to evaluate the distance between charges, such that:

`F = k*(q_1*q_2)/r^2 => r^2 = k*(q_1*q_2)/F`

Since the problem provides the force `F = 2.3 N` and the charges `q_1 = 40muC = 40*10^(-6)C = 4*10^(-5)C` and `q_2 = -50muC = -5*10^(-5)C` and replacing `8.99*10^9` for k, yields:

`r^2 = 8.99*10^9*20*10^(-10)/2.3`

`r^2 = 7.817 m^2 => r ~~ 2.8 m`

Hence, evaluating the distance r between charges, under the given conditions, yields ` r ~~ 2.8 m` .

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