# Calculus

Two electrical charges, one a positive charge A of magnitude a and the other a negative charge B of magnitude b, are loacted a distance c apart. A positively charged Particle P is situated on the line between A and B. Find where P should be put on so that the pull away from A towards B is minimal. Here assumee that the force from each charge is proportional to the strength of the source and inversely proportional to the square of the distance from the source.

Let x be the distance from P to A, and so c-x is the distance from P to B.
The net force acting upon P, while it is between A and B, is
F = k q [a/x^2 + b/(c-x^)2]
a and b are positive charge magnitud3es and q is the charge of P. k is a Boltzman contant. The force is a minimum when dF/dx = 0
-2 a/x^3 + 2 b/(c-x)^-3
(b/a) = [(c-x)/x]^3 = [(c/x)-1]^3
This can be solved for x/c in terms of b/a

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