Force Between Two Charges

Coulomb's Law

Two small charged particles separated by a distance of three meters are found to exert an attractive force of 8x10^-3N on each other. If the total charge on the two particles is 6 micro C, what is the charge on each particle?

We have two equations involving our two charges: the Coulomb Force Equation and the total charge equation:

|F| = F = -kQ₁Q₂/r² = 8x10^-3N

Q₁ + Q₂ = 6x10^-6C = Q

The minus sign is required in the force equation as we know that the charges must have opposite sign, but we want the magnitude of the electric force to be positive.

Rearranging the second equation gives:

Q₁ = Q - Q₂

Then, substituting this into the first yields:

-k (Q- Q₂) Q₂/r² = F

(Q*Q₂-Q₂²) = -r²F/k

Q₂² - Q*Q₂ - r²F/k = 0

Solving this quadratic, we get:

Q₂ = 7.12 micro C or -1.12 micro C

In these cases, the other charge is:

Q₁ = -1.12 micro C or 7.12 micro C

These two answers are equivalent, but opposite. This is to be expected as there is no information in this problem that would tell us which charge has which sign.