Increasing magnitude of the charge

1. Feb 9, 2010

sophia.m

1. The problem statement, all variables and given/known data

Four pairs of conducting spheres, all with the same radius, are shown in the figure, along with the net charge placed on them initially. The spheres in each pair are now brought into contact, allowing charge to transfer between them. Rank the pairs of spheres in order of increasing magnitude of the charge transferred. Indicate ties where appropriate. (Use only the symbols < and =, for example A < B = C.)

2. Relevant equations

F=kq1q2/r2

F=q1+q2/2

3. The attempt at a solution

Since I only get one chance to do this problem, I just want to make sure if my reasoning is correct or if the formula I am using correct.

What i think is:
A=-3C
B=4C
C=-2C
D= 14C

Increasing order: A<C<B<D

OR

Multplying:
A= 5C
B= 0
C=5C
D=195C

Increasing order: B<A=C<D

Any insight is appreciated.

2. Feb 9, 2010

rl.bhat

The problem is not clear. I can't see the picture.

3. Feb 9, 2010

sophia.m

I have attached the picture.

Thanks for the effort.

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4. Feb 9, 2010

rl.bhat

Find the charge transferred in each case irrespective of the sign of the charge.

5. Feb 9, 2010

sophia.m

When the pair of charged spheres are put in contact, the charge acquired will be (q1+q2) /2 each.

Thus, for pair A, the charge transferred is - 2q, for pair B it is 4q, for pair C it is - 3q and for pair D it is q. hence, the increasing order of magnitude of charge transferred is C < A < D < B.

Am I doing it correctly?

6. Feb 9, 2010

rl.bhat

the increasing order of magnitude of charge transferred is C < A < D < B.
This is not correct.
It should be
D<C<A<B

Last edited: Feb 9, 2010
7. Feb 9, 2010

sophia.m

Can you explain why? I don't get it.

8. Feb 9, 2010

sArGe99

When kept in contact, the potentials of the spheres equalize. Since the spheres are of same radius, this would mean that the charges on the spheres equalize.
As you correctly said, the final charge on each sphere will be Q1 + Q2 /2
Charge transferred = Q1 + Q2 /2 - Q2 (Final - Initial)
Q1 - Q2 /2.

Magnitude of charge transferred

A = 2q
B = 4q
C = 3q
D = q

Decreasing order
B > C > A > D

Note: In case of A, you can either say +2q has been transferred from sphere 1 to 2 or -2q from sphere 2 to 1.

9. Feb 9, 2010

sophia.m

Thank you very much! This is correct and I get it now. :)