Solution:

Given, four point charges of 20 uC each are placed on the x and y-axes at a distance of -4m.

Charge on the point charge: q = 100 uC

Position of the point charge: (0, 0, 3)m

We need to find the force acting on the point charge due to the four charges.

1. Calculation of Electric Field:

Electric field at point P(0, 0, 3) due to the four charges can be calculated using Coulomb's law.

Electric Field due to q1 at P(0, 0, 3) = kq1/r1^2

where, k = 9x10^9 Nm^2/C^2 is the Coulomb's constant

r1 = distance between q1 and P(0, 0, 3) = sqrt(3^2+4^2) = 5 m

q1 = -20 uC (negative sign indicates that it is a negative charge)

Thus, Electric Field due to q1 at P(0, 0, 3) = (9x10^9)(-20x10^-6)/(5^2) N/C

Similarly, Electric Field due to q2, q3, and q4 at P(0, 0, 3) can be calculated.

Electric Field due to q2 at P(0, 0, 3) = (9x10^9)(20x10^-6)/(5^2) N/C

Electric Field due to q3 at P(0, 0, 3) = (9x10^9)(20x10^-6)/(5^2) N/C

Electric Field due to q4 at P(0, 0, 3) = (9x10^9)(-20x10^-6)/(5^2) N/C

Net Electric Field at P(0, 0, 3) due to the four charges,

E = E1 + E2 + E3 + E4

E = (9x10^9)(-20x10^-6)/(5^2) N/C + (9x10^9)(20x10^-6)/(5^2) N/C + (9x10^9)(20x10^-6)/(5^2) N/C + (9x10^9)(-20x10^-6)/(5^2) N/C

E = 0 N/C

Thus, the net electric field at P(0, 0, 3) due to the four charges is zero.

2. Calculation of Force:

Force acting on the point charge can be calculated using the formula,

F = qE

where, q is the charge on the point charge and E is the electric field at the point.

Substituting the values, we get,

F = (100x10^-6)(0) N

F = 0 N

Thus, the force acting on the point charge is zero.

Answer: The force acting on the 100 uC point charge at (0, 0, 3)m is zero.

1.728 N