How to apply Coulomb's law for a system with a dielectric slab?

[sankalpmittal]

Homework Statement

Two similar point charges q₁ and q₂ are placed at a distance r apart in the air. A dielectric slab of thickness t(<<r) having dielectric constant K is placed between the charges. Calculate the coulomb force of repulsion between the charges.

Now assume that a slab of thickness half the separation between the charges and the Coulomb's repulsive force is reduced in the ratio 9:4. Calculate K for such a slab.

Homework Equations

Coulomb's law :

F=q₁q₂/4πεr²

where ε=ε_oK

The Attempt at a Solution

I am not sure. For such a system how should I apply Coulomb's law ? We have a dielectric slab between the system. So how to make that law apply here ?

I just thought that I have to transform the given system to its equivalent vacuum one, but how should I do that ?

Please help !

Thanks in advance...

 

[sankalpmittal]

Can someone help me please ? I am really clueless. :(

 

[Tanya Sharma]

Hi Sankalp

I just thought that I have to transform the given system to its equivalent vacuum one, but how should I do that ?

You have the right idea .

First convert the slab width 't' into effective air separation . Can you do that ?

 

[sankalpmittal]

Hi Sankalp



You have the right idea .

First convert the slab width 't' into effective air separation . Can you do that ?

Thanks..

If we hypothetically bring the two charges with the separation "t", then

q1q2/4πε_oKt² = q1q2/4πε_ox²

Solving we get x=√(K)t

Then in the actual system, effective separation is d-t+x ? Right ?

BTW, are you an IIT aspirant ?

 

[Tanya Sharma]

Thanks..

If we hypothetically bring the two charges with the separation "t", then

q1q2/4πε_oKt² = q1q2/4πε_ox²

Solving we get x=√(K)t

Correct.

Then in the actual system, effective separation is d-t+x ? Right ?

r-t+x

 

[sankalpmittal]

Correct.
r-t+x

Ya ya... I mistyped... I always do... d for distance...

Now with this information I solved both the parts completely...

Thanks a lot ! The answer matches with the key. :)