Easy 10 points, really.?

Question

Object A has a charge +2μC and object B has a charge of 6μC. Which statement is true?

I'm not sure about the condition of the 6μC charge, so please indicate the answer (a, b, c or d) in both conditions: (6μC and -6μC). THanks a lot!

A. Fab = - 3 Fba

B. Fab = - Fba

C. 3 Fab = - F ba

D. F ab = 3 F ba

Answer 1

B is correct. Here's why....

The force F = kqQ/r^2 between the charges (q and Q) r distance apart. But, and this is a big BUT, the sign of the force, F, is either plus (repelling) or negative (attracting) no matter which direction (ab or ba) you go between the two sources.

Further, there is but one force (F) between them, your answers other than B imply there are two forces Fab and Fba of different magnitudes; there are not as F = kqQ/r^2 clearly shows. That's one F for the two charges q and Q.

Visually, the force arrows from each charge of opposite sign are pointing inward to a point in between the charges when the force is attracting. We know this is true because the force F on each opposite sign charge is pulling the two of them together. Thus, from F = kqQ/r^2, we have a single force F < 0 when the q and Q charges are different signs.

Further, as the center of mass (between the two charges) is not moving, the force on each charge is equal and opposite in sign. This is true because, otherwise, the center of mass (CM) between the two charges would be accelerating as f = Fab + Fba > 0 would cause the CM to accelerate. But since CM is stationary (I presume), we have Fab + Fba = 0; so that Fab = -Fba, which is answer B. [Note: Fab = -Fba because Fab - Fab = 0 = Fab + Fba; so that Fab = -Fba QED.]

Conversely, the arrows are pointing outward from each charge when the single force (F) is repelling. Thus, F > 0 when q and Q have the same charge signs. Again, CM remains fixed; so that Fab + Fba = 0 and Fab = -Fba. [Or, since the two force vectors are reversed direction from the attraction case, we could write -(Fab + Fba) = 0 and still end up with Fab = -Fba.] Again, answer B is correct.

The point of B is that there is but one force (F), not two of different magnitudes. But that same force is acting on both charges, but in equal but opposite directions since the CM between them is not accelerating.

Answer 2

B

The forces will be of equal magnitude and opposite direction.

Changing the charge of one or both objects will not change this. it will only make both force magnitudes lesser or greater.

Answer 3

C!!