Question

Three point charges, q1, q2, and q3, lie along the x-axis at x = 0.0 cm, x = 3.0 cm, and x = 5.0 cm, respectively. Calculate the electric force on q2 if q1 = +6.0 ?C, q2 = +1.5 ?C, and q3 = -2.0 ?C.

Answer 1

The superposition principle basically states that the force on each particle is the vector sum of the forces exerted on it by all nearby charged particles. Since all of the charges line on the x-axis, we don't need to treat this as a vector problem. First, use Coulomb's law to determine the force that each charge exerts on each other charge:

Fij = k*qi*qj/r^2
where
Fij = the force that charge qi exerts on charge qj.
k = Coulomb constant =~9 * 10^9 N*m^2/C^2 (I'm assuming your charges are in units of C)
qi = charge of particle i
qj = charge of particle j
r = distance between particle i and j

For now let's ignore charges and just calculate the magnitude of the forces:
F12 = (9*10^9 N*m^2/C^2) * 6.0*10^-6 C * 1.5*10^-6 / (.03 m)^2 = 90 N (make sure you convert cm to m so your units will be consistent)
F13 = (9*10^9 N*m^2/C^2) * 6.0*10^-6 C * 2.0*10^-6 / (.05 m)^2 = 43 N
F23 = (9*10^9 N*m^2/C^2) * 1.5*10^-6 C * 2.0*10^-6 / (.02 m)^2 = 68 N

Charges q1 and q2 are both positive, so they will repel each other. F12 acts on q1 to the left, and on q2 to the right. Charge q1 and q3 are opposite charges, so they will attract each other. F13 acts on q1 to the right, and on q3 to the left. Charge q2 and q3 are opposite charges, so they will attract. F23 acts on q2 to the right and q3 to the left. So

Fnet1 = -90 N + 43 N = -47 N (to the left)
Fnet2 = 90 N + 68 N = 158 N (to the right)
Fnet3 = -43 N - 68 N = -111 N (to the left