Dependence of Coulomb's law on the medium

[Krushnaraj Pandya]

Homework Statement

I read in my textbook that the force exerted by a charged particle q1 on another charged particle q2 does not depend on the medium between them. Yet we multiply ε by ε(r) in coulomb's law when there is a medium present between the particles. Can someone please explain this contradictory things to me? Thank you.

Homework Equations

F=kq1q2/r^2
k=1/4πε*ε(r)

The Attempt at a Solution

Conceptual question

 

[Merlin3189]

I read in my textbook that the force exerted by a charged particle q1 on another charged particle q2 does not depend on the medium between them.

I think you may have been mis-informed, or your textbook simply does not consider this issue. Most elementary books don't.
See this link. http://autodock.scripps.edu/resources/science/coulombs_law
or https://www.tau.ac.il/~tsirel/dump/Static/knowino.org/wiki/Coulomb's_law.html
or http://www.schoolphysics.co.uk/age1.../Electrostatics/text/Coulomb's_Law/index.html

 

[Krushnaraj Pandya]

I think you may have been mis-informed, or your textbook simply does not consider this issue. Most elementary books don't.
See this link. http://autodock.scripps.edu/resources/science/coulombs_law
or https://www.tau.ac.il/~tsirel/dump/Static/knowino.org/wiki/Coulomb's_law.html
or http://www.schoolphysics.co.uk/age16-19/Electricity and magnetism/Electrostatics/text/Coulomb's_Law/index.html

Thank you very much, it seems from these links that it depends on the medium without a doubt. They were very informative.

 

[Merlin3189]

I'm no expert on this. It just seems obvious that ε₀ should apply only in vacuum or approximately in air, etc. So I looked for confirmation.
Interestingly, Hyperphysics, which I look to as an authoritative source, gives Coulombs law as if it applies only in a vacuum - no mention of ε or ε_r, only ε₀. Perhaps Coulomb never thought about this?
But whether it's his original law or not, the true relationship must involve ε_r when the medium is not a vacuum.

 

[Krushnaraj Pandya]

I'm no expert on this. It just seems obvious that ε₀ should apply only in vacuum or approximately in air, etc. So I looked for confirmation.
Interestingly, Hyperphysics, which I look to as an authoritative source, gives Coulombs law as if it applies only in a vacuum - no mention of ε or ε_r, only ε₀. Perhaps Coulomb never thought about this?
But whether it's his original law or not, the true relationship must involve ε_r when the medium is not a vacuum.

I have a slight memory of reading that the force due to the source charge doesn't change- rather the medium due to polarization(?*not sure) changes the net force on the test particle...I'm not sure about this, I just have a faint recollection

 

[Krushnaraj Pandya]

I have a slight memory of reading that the force due to the source charge doesn't change- rather the medium due to polarization(?*not sure) changes the net force on the test particle...I'm not sure about this, I just have a faint recollection

Does anyone have more insight on this? @Charles Link @Delta2

 

[Delta2]

I have a slight memory of reading that the force due to the source charge doesn't change- rather the medium due to polarization(?*not sure) changes the net force on the test particle...I'm not sure about this, I just have a faint recollection

Yes I think that is correct, the medium is polarized due to the charges and thus the electric field is different than if the medium was pure vacuum, and thus the net force on the particle is different than if the medium was pure vacuum.
So yes maybe strictly speaking your book is correct afterall, the coulomb force between two charges does not depend on the medium, but the net force that one charge will feel due to the presence of the other depends on the medium. The difference between the net force and the coulomb force is due to the sum of coulomb forces between the molecules of the polarized medium and the charge.

 

[Krushnaraj Pandya]

Yes I think that is correct, the medium is polarized due to the charges and thus the electric field is different than if the medium was pure vacuum, and thus the net force on the particle is different than if the medium was pure vacuum.
So yes maybe strictly speaking your book is correct afterall, the coulomb force between two charges does not depend on the medium, but the net force that one charge will feel due to the presence of the other depends on the medium. The difference between the net force and the coulomb force is due to the sum of coulomb forces between the molecules of the polarized medium and the charge.

Alright! seems like I haven't forgotten everything yet. What do I mark in an exam though? could I dispute it if they decided to say my answer is incorrect...by the way if you want to take a look at the jee paper for reference perhaps- here's a link
http://iitjee.vidyalankar.org/jee-main/JEE-MAIN-2018-Paper-and-Solution.pdf
Its easy enough...I just can't complete it in time

 

[Delta2]

Well it all depends how exactly the coulomb force is defined in your book.

If it is defined as the force that each charge feels due to the presence of the other in the vacuum, or it gives the formula $F=\frac{1}{4\pi\epsilon_0}\frac {q_1q_2}{r^2}$ then your book is correct and this force doesn't change since we say in the definition that it is the force in the vacuum.

However if your book defines the coulomb force in a way similar to the following text
"The force that each charge feels due to the presence of the other" then this force also depends on the medium in which the two charges are, since the medium gets polarized and the polarization changes the electric field that each charge feels due to the presence of the other comparing to the case that both charges where in vacuum. In this case with a medium present the formula $F=\frac{1}{4\pi\epsilon_r\epsilon_0}\frac{q_1q_2}{r^2}$ where $\epsilon_r$ the dielectric constant of the medium, is an approximation for where one of the two charges is negligible small and its electric field doesn't affect the polarization of the medium.