According to Coulomb's law, the electric force will be doubled if the separation of two equal charges is cut in half ? TRUE or FALSE ? Why?

1 Answer
Douglas K.
Feb 5, 2018

False. Please see the explanation.

Explanation:

Coulomb's Law in scalar form is:

#F = k_e(q_1q_2)/r^2#

Assume that the above is the force, #F#, corresponding original distance #r# between the two charges.

Now look at what happens to the force when we cut the distance in half by letting #r = 1/2r#

#F = k_e(q_1q_2)/(1/2r)^2#

#F = k_e(q_1q_2)/(1/4(r)^2)#

#F = k_e(4q_1q_2)/r^2#

Please observe that a factor of 4 has been introduced to the original. This means the the force is quadrupled (not doubled) when the distance between the two charges is cut in half.

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