Knowing that positive charges repel each other, we can say that charge q1 exerts a rightward electric force on charge q2, and charge q3 exerts a leftward electric force on charge q2.
The general equation for the electric force between two charges is:
F = kQq/r²
F = electric force, k = Coulomb's constant, Q & q = charges, r = distance between charges
Calculate the force between q1 and q2 with the given values:
k = 9×10⁹Nm²C⁻²
, Q = q1 = 2.00×10⁻⁵C, q = q2 = 3.80×10⁻⁵C, r = 1.00m
Plug in and solve for F:
F = 9×10⁹(2.00×10⁻⁵)(3.80×10⁻⁵)/(1.00)²
F = 6.84N
Calculate the force between q1 and q2 with the given values:
k = 9×10⁹Nm²C⁻²
, Q = q3 = 5.30×10⁻⁵C, q = q2 = 3.80×10⁻⁵C, r = unknown
Plug in and solve for F:
F = 9×10⁹(5.30×10⁻⁵)(3.80×10⁻⁵)/r²
F = 18.126/r²
The magnitude of the net force on q2 is the difference of the magnitude of the electric force due to q1 and the magnitude of the electric force due to q3:
6.84 - 18.126/r²
The magnitude of the net force is 5.56N, so let us set up the following equation and solve for r, the distance between q2 and q3:
6.84 - 18.126/r² = 5.56
18.126/r² = 1.28
r² = 14.161
r = 3.76m
q2 is 3.76m away from q3.
