# Electric field formula vs coulombs law, contradiction?

• Kurret
In summary, the conversation discusses the concept of electric fields and forces between two charged plates. It explains that the force on a particle between two plates is independent of its position, regardless of the distance between the plates. The conversation also explores different equations for capacitance and the electric field, and how they relate to the distance between the plates. The limitations of these equations are also discussed, particularly in cases where the plates are not significantly larger than the distance between them. These limitations may explain some of the discrepancies in results discussed in the conversation.

#### Kurret

1) between two charged plates, the electric field is given by E=U/d=F/Q->F=QE
that means that the force on a particle between these two plates is independant on the position between them. But consider that you have two plates separated by a huge distance, then the force is constant wherever we place a charged particle between the plates. But if we use coulombs law and treat the plates as other charged particles we will get different results. How come?

2) in a plate? condensator we have C=eA/d (e=permitivity constant, d=distance, A=the plates area)
we also have C=Q/U
putting these equal to each other gives:
eA/d=Q/U -> Q/(eA)=U/d=E
ie the electrical field, and the force on a prarticle in between the plates, is independant on the distance between the plates. I can't really get the logic in this one. for example let's say we have two charged plates with a distance of 1 cm from each other, and then we move one plate away to the andromeda galaxy. That the force on a particle wherever in between these two plates still should be the same as with the distance of 1 cm is just absurd.

Can someone explain these results? I am only still in high school so I haven't studied so much advanced physics. Is it maybe because the formula for the electric field is just an apporximation of the real world?

Last edited:
These are reasonable questions. All of these parallel plate capacitor equations only work when the dimension of the plates is much greater than the spacing between the plates. With these constraints, the cases you describe follow as the formulas say they should.

I can understand your confusion and concerns about the apparent contradiction between the electric field formula and Coulomb's law. However, it is important to note that both of these equations are derived from different assumptions and are used in different scenarios.

The electric field formula, E=U/d=F/Q, is used to calculate the electric field between two parallel plates that are infinitely large and uniformly charged. This formula assumes that the electric field is constant and independent of the distance between the plates. This is a simplified model and is only applicable in certain situations, such as in a parallel plate capacitor.

On the other hand, Coulomb's law is used to calculate the electrostatic force between two point charges. This law assumes that the charges are point charges and that the force between them follows an inverse square relationship with distance. This is a more general formula and is applicable in a wider range of scenarios, such as between two charged particles.

In the case of the two charged plates, the electric field formula is an approximation and does not take into account the finite size of the plates. As you correctly pointed out, when the plates are separated by a large distance, the force between them calculated using Coulomb's law will be different from the force calculated using the electric field formula. This is because the electric field formula does not account for the changes in the electric field caused by the finite size of the plates.

To further explain the results, it is important to also consider the concept of capacitance. In a parallel plate capacitor, the capacitance (C) is a measure of the ability of the plates to store charge. It is directly proportional to the area of the plates (A) and inversely proportional to the distance between them (d). This is why, in the second scenario you mentioned, when the distance between the plates is increased, the capacitance decreases.

In summary, there is no contradiction between the electric field formula and Coulomb's law. They are both valid equations derived from different assumptions and are used in different scenarios. The electric field formula is an approximation and may not hold true in all situations, while Coulomb's law is a more general formula that can be applied in a wider range of scenarios. I hope this explanation helps to clarify the results for you. Keep up your curiosity and interest in physics, and continue to ask questions and seek answers!

## 1. What is the difference between the electric field formula and Coulomb's law?

The electric field formula is used to calculate the strength and direction of an electric field at a specific point in space, while Coulomb's law is used to calculate the force between two electrically charged particles.

## 2. Why do the electric field formula and Coulomb's law sometimes seem contradictory?

The electric field formula and Coulomb's law can seem contradictory because they are based on different mathematical models. The electric field formula is derived from the concept of the electric field, while Coulomb's law is derived from the concept of the electric force between charged particles.

## 3. Which one is more accurate, the electric field formula or Coulomb's law?

Both the electric field formula and Coulomb's law are accurate in their respective contexts. The electric field formula is more useful for calculating the electric field at a specific point, while Coulomb's law is more useful for calculating the force between two charged particles.

## 4. Can the electric field formula and Coulomb's law be used interchangeably?

No, the electric field formula and Coulomb's law cannot be used interchangeably. While they both deal with electric fields and forces, they are based on different principles and cannot be used in place of each other.

## 5. How can we reconcile the discrepancies between the electric field formula and Coulomb's law?

The discrepancies between the electric field formula and Coulomb's law can be reconciled by understanding that they are based on different mathematical models and are used for different purposes. Additionally, they both become more accurate as the distance between charged particles decreases.