Final answer:
To find the magnitude of the net force on a charge, calculate the forces exerted by each individual charge and then add them up using Coulomb's Law. In this case, there is a charge of 1.20 mC at the origin, a charge of 2.40 mC at (3.0m,0), and a charge of -5.70 mC at (0,4.0m). Calculate the forces exerted by each charge and sum them to find the net force on the charge at the origin.
Step-by-step explanation:
To find the magnitude of the net force on a charge, we need to calculate the forces exerted by each individual charge and then add them up. The formula for calculating the electric force between two charges is given by Coulomb's Law:
F = k * (q1 * q2) / r^2
where F is the force, k is Coulomb's constant (9 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between them.
In this case, we have a charge of 1.20 mC at the origin, a charge of 2.40 mC at (3.0m,0), and a charge of -5.70 mC at (0,4.0m).
The net force on the charge at the origin can be calculated by summing up the forces exerted by the other two charges:
Fnet = F1 + F2
where F1 is the force exerted by the charge at (3.0m,0), and F2 is the force exerted by the charge at (0,4.0m).
Calculating the forces:
F1 = k * ((1.20 * 10^-3 C) * (2.40 * 10^-3 C)) / (3.0 m)^2
F2 = k * ((1.20 * 10^-3 C) * (-5.70 * 10^-3 C)) / (4.0 m)^2
Adding up the forces:
Fnet = F1 + F2
Finally, we can calculate the magnitude of the net force by taking the absolute value of Fnet.