How can Coulomb's Law be used to find the force between a charge and a surface?

[shotikokobaxi]

Homework Statement

We have a charge Q and it's h metres far from the flat surface. Find the force with which acts on the Q charge by the surface
The answer is: F=kQ²/4h² i couldn't get it, please help me.

Homework Equations

The Attempt at a Solution

 

[gneill]

Homework Statement

we have a charge Q and it's h metres far from the flat surface. Find the force with which acts on the Q charge by the surface
The answer is: F=kQ²/4h² i couldn't get it, please help me

Wow! No need to shout (Big loud font)

Welcome to Physics Forums, shotikokobaxi.

What formula(s) are appropriate here? Is the flat surface a conducting surface? If so, what analysis technique is appropriate for calculating the effects of an induced charge?

 

[shotikokobaxi]

Wow! No need to shout (Big loud font)

Welcome to Physics Forums, shotikokobaxi.

What formula(s) are appropriate here? Is the flat surface a conducting surface? If so, what analysis technique is appropriate for calculating the effects of an induced charge?

we use kulon's force F=kq²/r² the question is to find the force with which the surface (which hasn't any charges) acts on the Q charge

 

[gneill]

we use kulon's force F=kq²/r² the question is to find the force with which the surface (which hasn't any charges) acts on the Q charge

Yes, that's what we call Coulomb's force law for electric charges. It is applicable, but there's a special technique which can be used for cases where one charge induces a charge in an otherwise uncharged conducting surface as you have here. Look up "the method of image charges".

 

[Nickie]

I understand that electricity is a fundamental force in nature and is responsible for the movement of charged particles. In this problem, we have a charge Q located h meters away from a flat surface. We are asked to find the force with which the surface acts on the charge Q. To do this, we can use Coulomb's Law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

In this case, we have a single charge Q and a surface, which can be considered as a large number of charges. Therefore, we can use the surface charge density, σ, to represent the surface's charge. The formula for surface charge density is σ = Q/A, where Q is the total charge on the surface and A is the surface area.

Now, using Coulomb's Law, we can calculate the force between the charge Q and the surface. The formula for Coulomb's Law is F = kQq/r^2, where k is the Coulomb's constant, Q is the charge of the particle, q is the charge of the surface, and r is the distance between the two charges.

In this case, we can replace q with σA, since the surface charge density represents the charge per unit area on the surface. Therefore, the formula becomes F = kQσA/r^2.

Substituting Q = σA, we get F = kQ^2/r^2. Since the distance between the charge and the surface is h, we can replace r with h, giving us the final formula F = kQ^2/h^2.

This is the force with which the surface acts on the charge Q. To get the final answer, we need to plug in the values of Q and h into the formula. I hope this explanation helps you understand the solution to the problem.