# Contradiction in a charge redistribution problem

## Homework Statement

There are two metallic spheres, of same kind ,separeted from one another .One of them has charge 6 C wheras the another one is neutral.They are brought in contact for a long time.Then they are separeted again.Now what is the charges of the spheres?

: [/B]

## The Attempt at a Solution

: [/B]
I assume that this charge will redistribute equally between the two sphers.so The charge of each sphere is +3.but in some references,i found the charges will remain +6,0.
Thanks

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kuruman
Homework Helper
Gold Member

## Homework Statement

There are two metallic spheres, of same kind ,separeted from one another .One of them has charge 6 C wheras the another one is neutral.They are brought in contact for a long time.Then they are separeted again.Now what is the charges of the spheres?

: [/B]

## The Attempt at a Solution

: [/B]
I assume that this charge will redistribute equally between the two sphers.so The charge of each sphere is +3.but in some references,i found the charges will remain +6,0.
Thanks
Are you saying that you found references claiming that one conductor will retain its charge and the other will be neutral? Can you provide these references?

ZapperZ
Staff Emeritus
I assume that this charge will redistribute equally between the two sphers.so The charge of each sphere is +3.but in some references,i found the charges will remain +6,0.
Thanks
What "some references"?

In this forum, you simply can't say that without providing clear and exact citation.

Zz.

RPinPA
Homework Helper
The principle is that a conductor is an equipotential. Every part of the conductor will be at the same potential. When touching, the charge will redistribute so that both spheres are at the same potential.

I assume that this charge will redistribute equally between the two sphers.so The charge of each sphere is +3
If they are identical in radius, then yes, this is the equipotential situation. If they are not, then you would have to work out what distribution of charge gives you the same potential on both spheres using the expression for potential of a charged conducing sphere.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potsph.html

in some references,i found the charges will remain +6,0.
That is not going to be the solution for any situation with two conducting spheres. You misread something or misremembered something.

Yeah.i misunderstand the article .sorry for creating confusion

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haruspex
Homework Helper
Gold Member
If they are identical in radius, then yes, this is the equipotential situation. If they are not, then you would have to work out what distribution of charge gives you the same potential on both spheres using the expression for potential of a charged conducing sphere.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potsph.html
Not relevant to this thread, but that link does not answer the charge distribution for unequal conducting spheres in contact. It is a much subtler problem.
According to https://pdfs.semanticscholar.org/2138/05eeb99f6b0212fbc227d711bd4f4cae85eb.pdf, Maxwell (1891) showed the charge ratio to be ##\frac{\gamma+\psi(\frac b{a+b})}{\gamma+\psi(\frac a{a+b})}##, where ##\psi(z) = \frac d{dz} \ln \Gamma(z)## and ##\gamma = −\psi(1)## = 0.5772 ... is Euler’s constant. This ratio can be approximated as ##(\frac ab)^2(\frac{\pi^2}6)^\frac{a−b}{a+b}##.
(I may have been inconsistent in whether that's Qa/Qb or the other way up.)

gneill
kuruman
Homework Helper
Gold Member
Not relevant to this thread, but that link does not answer the charge distribution for unequal conducting spheres in contact.
I interpreted OP's label of the spheres as "same kind" to mean "identical". My reasoning is that, assuming that this problem is well-crafted, the ratio of radii will be given. Perhaps OP can post the question exactly as given? If the original question is in a language other than English, the possibility exists that something can be lost in translation.

haruspex