Calculating Electrostatic Force on a Charged Particle Near a Flat Surface

[huzzi.123]

Homework Statement

A particle of charge +q is a distance r away from a charged flat surface and experiences a force of magnitude F pulling it toward the surface. What is the magnitude of the force exerted on a particle of charge +q that is a distance 2r from the surface?

Homework Equations

F=KQ1Q2/r^2
E=F/q
E=Kq/r^2

The Attempt at a Solution

The coulomb's formula seems to fit in i.e F=KQ1Q2/r^2
but I stopped solving it further since Q2 or the value of any other charge isn't mentioned in a question. Anyone please help me do this question?

Thanks.

 

[kontejnjer]

Well the question seems rather ambiguous as it doesn't say whether the plate is infinite in area, and if it isn't, just how large is it compared to the distance r. If you assume it's the former, and also assume the charge distribution on it is homogenous, you should start by finding the electric field due to the plate at an arbitrary distance from it using Gauss's law, and then find the force using the equation \vec{F}=q\vec{E} (you can also find the field using Coulomb's law, but the procedure is a bit more complicated).

 

[huzzi.123]

You mean by applying the formula ; E= charge density/permittivity?

 

[Varadha]

The answer should be F/4, isn't it?

 

[CAF123]

You mean by applying the formula ; E= charge density/permittivity?

I agree with kontejnjer: If you assume an infinite plate with uniform charge distribution, then you can find the E-field it produces using Gauss' Law. It is not quite the result you stated above.

 

[huzzi.123]

That's what I got after working out my intuition but unfortunately this isn't a right answer.