What Was the Initial Charge on Sphere A in the Conducting Spheres Problem?

[a85liz]

Homework Statement

Figure 21-36 shows four identical conducting spheres that are actually well separated from one another.

Figure 21-36
Sphere W (with an initial charge of zero) is touched to sphere A and then they are separated. Next, sphere W is touched to sphere B (with an initial charge of -29e) and then they are separated. Finally, sphere W is touched to sphere C (with an initial charge of +43e), and then they are separated. The final charge on sphere W is +13e. What was the initial charge on sphere A?

Homework Equations

don't know

The Attempt at a Solution

I tried working backwards from the known charge and using the formula Q=.5(q1-q2). I am sure I am missing something simple, but I can not figure this problem out.

 

[LowlyPion]

Homework Statement

Figure 21-36 shows four identical conducting spheres that are actually well separated from one another.

Sphere W (with an initial charge of zero) is touched to sphere A and then they are separated. Next, sphere W is touched to sphere B (with an initial charge of -29e) and then they are separated. Finally, sphere W is touched to sphere C (with an initial charge of +43e), and then they are separated. The final charge on sphere W is +13e. What was the initial charge on sphere A?

I tried working backwards from the known charge and using the formula Q=.5(q1-q2). I am sure I am missing something simple, but I can not figure this problem out.

Welcome to PF.

Maybe try working forwards? After touching A you know W carries 1/2A.

You know what B carries, so after touching B you have 1/2(1/2A + (-29))

So develop the formula for after touching C and knowing the final value, solve for A.