What are the forces (in N) on two charges of +0.400 C and
−3.00 C, respectively, if they are separated by a distance of 4.00 m?
The force between two charges can be calculated using Coulomb's law:
F = k * |q1 * q2| / r^2
where:
F is the force between the charges
k is the Coulomb constant (k ≈ 8.9875 x 10^9 N m^2/C^2)
q1 and q2 are the magnitudes of the two charges (+0.400 C and -3.00 C)
r is the distance between the charges (4.00 m)
First, let's calculate the force between the +0.400 C and -3.00 C charges:
F = (8.9875 x 10^9 N m^2/C^2) * |+0.400 C * -3.00 C| / (4.00 m)^2
F = (8.9875 x 10^9) * 1.2 / 16
F = 6.740625 x 10^8 / 16
F = 4.2128906 x 10^7 N
The magnitude of the force between the charges is 4.2128906 x 10^7 N.
Therefore, the force on the +0.400 C charge is 4.2128906 x 10^7 N and the force on the -3.00 C charge is -4.2128906 x 10^7 N (equal in magnitude but opposite in direction).