How Does Charge Redistribution Affect Forces in a Triangular Sphere System?

[Shatzkinator]

Homework Statement

In the figure 21-40, three identical conducting spheres form an equilateral triangle of side length d = 24.0 cm. The sphere radii are much smaller than d and the sphere charges are qA = -3.45 nC, qB = -3.91 nC, and qC = +6.09 nC. (a) What is the magnitude of the electrostatic force between spheres A and C? The following steps are taken: A and B are connected by a thin wire and then disconnected; B is grounded by the wire, and the wire is then removed; B and C are connected by the wire and then disconnected. What now are the magnitudes of the electrostatic force (b) between spheres A and C and (c) between spheres B and C?
http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c21/fig21_41.gif

Homework Equations

F = kq1q2/r^2

The Attempt at a Solution

I got 3.28 x 10^-6 N for part A... not sure what to do for B and C

 

[LowlyPion]

... not sure what to do for B and C

Follow the subsequent steps. When A and B are connected what charge ends on each? Then B is rounded so the charge on B is now 0. Now B and C are connected and you end up with how much charge on B and C?

Now it looks like you're back to calculating forces again.

 

[nlightner]

I would like to clarify that conservation of charge is a fundamental principle in physics that states that electric charge cannot be created or destroyed, only transferred from one object to another. This means that the total amount of charge in a closed system remains constant.

In this scenario, we can use the equation F = kq1q2/r^2 to calculate the electrostatic force between spheres A and C. Plugging in the given values, we get a force of 3.28 x 10^-6 N. This is the force before any changes are made to the system.

When spheres A and B are connected by a wire and then disconnected, the total charge in the system remains the same but is redistributed between the two spheres. This means that the charges on spheres A and B will now be equal and opposite, resulting in a net charge of zero. This also means that there will be no electrostatic force between spheres A and B.

Next, when B is grounded and then disconnected, the charge on sphere B will be neutralized. This does not affect the charges on spheres A and C, so the electrostatic force between them will remain the same at 3.28 x 10^-6 N.

Finally, when spheres B and C are connected and then disconnected, the charges on these spheres will redistribute, resulting in a net charge of -3.91 nC on sphere B and +3.91 nC on sphere C. This will result in a new electrostatic force between spheres B and C, which can be calculated using the same equation. The force will be equal in magnitude to the force between spheres A and C, but in the opposite direction.

Therefore, the answers for parts (b) and (c) are 3.28 x 10^-6 N and -3.28 x 10^-6 N, respectively. It is important to note that these answers assume that the spheres are point charges and that the distance between them remains constant throughout the changes in the system.