# How far from q1 should the third charge be placed so that the net electric force on the third charge is minimized?

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Two charges q1=Q and q2=-8Q are L distance apart. A third charge is to be
placed on the line between the two charges. How far from q1 should the third charge be placed so that the net electric force on the third charge is minimized?

Answer : x=L/3

Why?
asked Sep 10, 2014

## 1 Answer

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Any charge placed in between two charges of opposite sign will be subject to a forces with the same direction from the original two charges. However, if the charge is placed outside of the original two charges, it will experience a force from each in opposite directions.

With this information, we can look at the total electric field created from the charges: $E = \frac{kq1}{x^2} + \frac{kq2}{(x-L)^2}$. The minimum possible net electric field will be when $E = 0$. Simply solve the equation for $x$ and you should find the result.

answered Sep 10, 2014 by (2,140 points)