The Electric Field Above a Plane: Have I Made a Wrong Assumption?

In summary, the equation E=kQ is often used to represent the electric field above a plate, as it follows the general trend of being proportional to 1/r^2 for a point and 1/r for a line. However, this equation is not commonly found elsewhere and it can be difficult to understand why the distance from the plate does not affect the strength of the field. In the case of two parallel plates, the principle of superposition would suggest that the field would be E=2kQ, but other equations such as E=V/d and C=Q/V are used to represent the field. Additionally, the assumption of A=4\pi r^2 does not apply for a plate extending to infinity, and instead
  • #1
21joanna12
126
2
I'm a bit confused about the electric field above a plate. First, I have come across the equation [itex]E=kQ[/itex] http://www.sparknotes.com/testprep/books/sat2/physics/chapter13section3.rhtml which in many ways makes sense to me because around a point the field would be proportional to [itex]1/{r^2}[/itex], and then for a line it would be proportional to [itex]1/{r}[/itex] etc, however I have not come across this formula anywhere else and am finding it hard to understand why moving away from the plate would not have any impact at all on the strength of the force on a changed partcle. Also, if this were the case then I would expect the field between two parallel plates to be [itex]E=2kQ[/itex] due to the principle of superposition. However I know from elsewhere that the E field between two parallel plates is [itex]E=V/d[/itex] and for a capacitor [itex]C=Q/V[/itex], and in the case of just air between the plates, [itex]C=\epsilon A/d[/itex], so putting that together I get that [itex]E=kQ/r^2[/itex]...

Have I made a wrong assumption somewhere?

Thank you!

EDIT: Sorry, for the last part I used [itex]A=4\pi r^2[/itex] which probably will not apply here. In that case, I am not sure what to do for the last part...
 
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  • #2
The plate is a plane, extending out to infinity so there are no edge effects. The plane carries charge uniformly distributed. Field lines from these charges space themselves apart and never cross each other, so the only possible field lines arrangement is all perpendicular to the plane, like the hairs on the back of a frightened cat. These field lines extend out to infinity and remain parallel to each other. So no matter how far away from the plane, the field strength is uniform and undiminished.

Your equations were looking good until the last where r leapt in unheralded and uninvited!
 
  • #3
NascentOxygen said:
The plate is a plane, extending out to infinity so there are no edge effects. The plane carries charge uniformly distributed. Field lines from these charges space themselves apart and never cross each other, so the only possible field lines arrangement is all perpendicular to the plane, like the hairs on the back of a frightened cat. These field lines extend out to infinity and remain parallel to each other. So no matter how far away from the plane, the field strength is uniform and undiminished.

Your equations were looking good until the last where r leapt in unheralded and uninvited!
Thank you for your reply! The thing is I do not know how to get rid of the r. If my equations were to work out, A would have to be [itex]2\pi[/itex]... And I have no idea why this would be the case. The only thing I can think of is that I have approached the question wrong and talking about the charge and area of the plate does not make sense. Instead I should be using the charge per unit area... Could that be it?
 

1. What is an electric field above a plane?

The electric field above a plane is a region in space where a charged particle would experience a force due to the presence of an electric charge on the plane. It is a vector quantity, meaning it has both magnitude and direction.

2. How is the electric field above a plane calculated?

The electric field above a plane can be calculated using Coulomb's law, which states that the electric field at a point is equal to the force between two charges divided by the distance between them squared. In the case of a plane, the formula becomes E = σ/2ε0, where σ is the surface charge density and ε0 is the permittivity of free space.

3. Is the electric field above a plane uniform?

Yes, the electric field above a plane is uniform, meaning it has the same magnitude and direction at every point above the plane. This is because the plane has an infinite extent and the charge is spread out evenly over the entire surface, resulting in a constant electric field.

4. How does the distance from the plane affect the electric field?

The electric field above a plane is directly proportional to the distance from the plane. This means that as the distance increases, the electric field decreases. This is due to the inverse square relationship in Coulomb's law, where the force between two charges decreases as the distance between them increases.

5. Can the electric field above a plane be negative?

Yes, the electric field above a plane can be negative. This occurs when the surface charge density on the plane is negative, resulting in an electric field with a direction opposite to that of a positive charge. However, in most cases, the electric field above a plane is considered to be positive, as the surface charge density is usually positive.

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