The force between two charges can be calculated using Coulomb's law, which states that the force (F) between two charges (q1 and q2) is proportional to the product of their charges and inversely proportional to the square of the distance (r) between them:
F = k * (q1 * q2) / r^2
where k is Coulomb's constant (9 x 10^9 N m^2 C^-2).
In this problem, we have two equal and opposite charges, so we can assume that q1 = -q2 = q. The distance between them is 40 mm, which is 0.04 m. We are given that the force between them is 0.5 N. Therefore, we can set up an equation:
0.5 N = k * (q * q) / (0.04 m)^2
Simplifying and solving for q:
q^2 = (0.5 N * (0.04 m)^2) / k
q^2 = (0.5 N * (0.04 m)^2) / (9 x 10^9 N m^2 C^-2)
q^2 = 8.88 x 10^-12 C^2
q = sqrt(8.88 x 10^-12 C^2)
q = 2.98 x 10^-6 C
Therefore, the magnitude of each charge is 2.98 x 10^-6 C.