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