Two point charges are located on the positive x-axis of a coordinate system. Charge q1 = 1.0 nC is 2.0 cm from the origin and charge q2 = -3.0 nC is 4.0 cm from the origin. What is the total force exerted by these two charges on a charge q3 = 5.0 nC located at the origin? Neglect gravitational force.

To find the total force exerted by the two charges on charge q3, we need to calculate the forces exerted by each individual charge and then add them together. The force between two point charges can be calculated using Coulomb's Law: $$F = (k * |q-{1} * q-{2€|) / r^{2}$$ Where: - F is the force between the charges, - k is the electrostatic constant with a value of 8.99 x 10^9 Nm^2/C^2, - q1 and q2 are the magnitudes of the charges, and - r is the distance between the charges. Considering the charges and their distances: Charge q1 = 1.0 nC Distance from the origin to q1 = 2.0 cm = 0.02 m Charge q2 = -3.0 nC Distance from the origin to q2 = 4.0 cm = 0.04 m Charge q3 = 5.0 nC (located at the origin) First, let's calculate the force between q1 and q3: F1 = (k * |q1 * q3|) / r1^2 F1 = (8.99 x 10^9 Nm^2/C^2 * |1.0 x 10^-9 C * 5.0 x 10^-9 C|) / (0.02 m)^2 F1 = (8.99 x 10^9 Nm^2/C^2 * 5.0 x 10^-18 C^2) / (0.04 m^2) F1 = (44.95 x 10^-9 N * m^2) / 0.0016 m^2 F1 = 28.09375 N Next, let's calculate the force between q2 and q3: F2 = (k * |q2 * q3|) / r2^2 F2 = (8.99 x 10^9 Nm^2/C^2 * |-3.0 x 10^-9 C * 5.0 x 10^-9 C|) / (0.04 m)^{2}$$ $$F-{2} = (8.99 x 10^{9} Nm^{2}/C^}2 }* 15.0 x 10^{-18} C^{2}) / (0.04 m^{2}) $$F_{2}= (134.85 x 10^}-9} N * m^{2}) / 0.0016 m^2$$ F2 = 84.28125 N Finally, we can calculate the total force: Total force = F1 + F2 Total force = 28.09375 N + 84.28125 N Total force = 112.375 N Therefore, the total force exerted by the two charges on charge q3 located at the origin is 112.375 Newtons.