Understanding charge transfer on metal spheres. Help please

[sitthegamsat]

Homework Statement

I would really appreciate help understanding how the answer is reached in this question:

Setting the scene: three metal sphere's are in fixed positions R (+Q), S (+2Q) and T (+3Q):

+Q +2Q +3Q
*--------------**-------------------------***
R S T

The distance between R and S is d1 and distance between S and T is d2. d2 = sq. root of 3*d1.

A small metal sphere carrying a charge of -2Q is first brought into contact with the sphere at R (+Q), and then into contact with the sphere at S (+2Q) and finally into contact with sphere T (+3Q). After making contact with the three spheres, in the stated order, the charge on the sphere at T is:

A: +3Q
B: +15Q/4
C: +15Q/8
D: +4Q

Homework Equations

? Perhaps F = K Q/r (squared)

The Attempt at a Solution

The solution to this question is C: +15Q/8

I would really really appreciate it if someone could explain how this answer is achieved. Is it perhaps charge accumulation from conduction in some way??

Thanks

 

[ehild]

Supposing that the radii of the circles are the same and very small with respect to d1, the charge shares equally between two circles in contact.

ehild

 

[sitthegamsat]

Thanks for the reply. I am still confused as to where the number 15Q comes from. If the charge is shared on the first contact does the one that is moved have 0.5+Q and -Q; then on the next contact it shares 2.5 +Q charge between two balls... how do we get the answer of +15Q/8?

Thanks again and further explanation would be much appreciated

 

[ehild]

If the charge is shared on the first contact does the one that is moved have 0.5+Q and -Q; then on the next contact it shares 2.5 +Q charge between two balls... how do we get the answer of +15Q/8?

Thanks again and further explanation would be much appreciated

If the charge is shared between two equivalent spheres than both of them will have the same charge after the contact.

ehild

 

[rwisz]

I would be happy to provide some insight into understanding charge transfer on metal spheres.

Firstly, let's start with the concept of charge transfer. Charge transfer occurs when two objects come into contact and one object has a higher or lower charge than the other. This results in the transfer of charge between the two objects until they reach a state of equilibrium, where they have the same charge.

In this scenario, we have three fixed metal spheres with charges of +Q, +2Q, and +3Q, respectively. This means that the total charge in the system is +6Q (Q+2Q+3Q). Now, when a small metal sphere with a charge of -2Q is brought into contact with the sphere at R (+Q), it will transfer charge until it reaches equilibrium with the sphere at R. This means that the charge on the small sphere will become +Q, and the charge on the sphere at R will become -Q (-Q+Q=0).

Next, the small sphere is brought into contact with the sphere at S (+2Q). Again, charge will transfer until equilibrium is reached, resulting in the charge on the small sphere becoming +2Q and the charge on the sphere at S becoming -2Q (-2Q+2Q=0).

Finally, the small sphere is brought into contact with the sphere at T (+3Q). Following the same process, the charge on the small sphere will become +3Q and the charge on the sphere at T will become -3Q (-3Q+3Q=0).

Now, let's look at the final charge on each sphere. The sphere at R started with a charge of +Q, but after coming into contact with the small sphere, it now has a charge of -Q. The sphere at S started with a charge of +2Q, but after coming into contact with the small sphere twice, it now has a charge of -2Q. And finally, the sphere at T started with a charge of +3Q, but after coming into contact with the small sphere three times, it now has a charge of -3Q.

To find the final charge on the sphere at T, we can use the equation Q=Q0*e^(kt), where Q0 is the initial charge, k is a constant, and t is the number of times the small sphere has come into contact with the larger sphere. In this case, t=3