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?
To calculate the forces on the two charges, we can use Coulomb's law:
F = k * |q1 * q2| / r^2
where:
F = force
k = Coulomb's constant (8.99 x 10^9 N*m^2/C^2)
q1 = charge 1 (+0.400 C)
q2 = charge 2 (-3.00 C)
r = distance between the charges (4.00 m)
First, let's calculate the force on charge 1 (+0.400 C) due to charge 2 (-3.00 C):
F1 = (8.99 x 10^9) * |(+0.400) * (-3.00)| / (4.00)^2
F1 = (8.99 x 10^9) * 1.20 / 16
F1 = 6.74 x 10^8 / 16
F1 = 4.22 x 10^7 N
Therefore, the force on the +0.400 C charge due to the -3.00 C charge is 4.22 x 10^7 N.
Next, let's calculate the force on charge 2 (-3.00 C) due to charge 1 (+0.400 C):
F2 = (8.99 x 10^9) * |(-3.00) * (+0.400)| / (4.00)^2
F2 = (8.99 x 10^9) * 1.20 / 16
F2 = 6.74 x 10^8 / 16
F2 = 4.22 x 10^7 N
Therefore, the force on the -3.00 C charge due to the +0.400 C charge is 4.22 x 10^7 N.
In summary, the force on the +0.400 C charge due to the -3.00 C charge is 4.22 x 10^7 N, and the force on the -3.00 C charge due to the +0.400 C charge is also 4.22 x 10^7 N.