Increasing magnitude of the charge

AI Thread Summary
The discussion revolves around determining the order of charge transferred between pairs of conducting spheres after they come into contact. The correct approach involves calculating the final charge on each sphere using the formula (Q1 + Q2) / 2, leading to the conclusion that the magnitude of charge transferred is A = 2q, B = 4q, C = 3q, and D = q. The increasing order of charge transferred is C < A < D < B. Participants clarify that when spheres are in contact, their potentials equalize, resulting in charge redistribution. The final consensus confirms the correct order and understanding of the charge transfer process.
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Homework Statement



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.)

19-31b.gif


Homework Equations



F=kq1q2/r2

F=q1+q2/2


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.
 
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The problem is not clear. I can't see the picture.
 
rl.bhat said:
The problem is not clear. I can't see the picture.

I have attached the picture.

Thanks for the effort.
 

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Find the charge transferred in each case irrespective of the sign of the charge.
 
rl.bhat said:
Find the charge transferred in each case irrespective of the sign of the charge.

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?
 
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:
rl.bhat said:
the increasing order of magnitude of charge transferred is C < A < D < B.
This is not correct.
It should be
D<C=A<B


Can you explain why? I don't get it.
 
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.
 
sArGe99 said:
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.

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