If all the charges are 15 cm from the origin (the crossing point of the vertical and horizontal lines) in the above figure and Q = +3.0 $\mu$C, then calculate the magnitude of the net force on a charge of +Q placed at the origin.

Question

Quizplus · Accepted Answer

Using Coulomb's Law, we can find the force between each charge and the charge at the origin:

F1 = k(Q)(Q)/(0.15)^2 = 720Q N
F2 = k(Q)(Q)/(0.15)^2 = 720Q N
F3 = k(Q)(Q)/(0.15)^2 = 720Q N

Since F1 and F3 are at opposite angles to F2, we can use the Pythagorean Theorem to find the net force:

Fnet = sqrt((F1^2 + F3^2) - F2^2) = sqrt((720Q)^2 + (720Q)^2 - (720Q)^2) 
     = sqrt(2(720Q)^2) = 1018.6 N ≈ 26.0 N

Therefore, the magnitude of the net force on a charge of +Q placed at the origin is 26.0 N (choice C).

If All the Charges Are 15 Cm from the Origin μ\muμ

If All the Charges Are 15 Cm from the Origin $\mu$