# Electrical force on parallel plates

• orthovector
In summary, during a lecture, the professor presented a scenario where two parallel plates with equal charges were placed on top of each other. Despite the electric field between the plates canceling out, the plates still exert a force on each other according to the formula F = sigma^2/2epsilon. This is due to the fact that the electric field within the plates is 0, but the charges on the plates still repel each other. This phenomenon can be explained by considering the distribution of charges on the plates, which will gather on the surface and become denser on sharper surfaces.

#### orthovector

In lecture, my professor showed us something peculiar.

2 parallel plates with equal charges lie close on top of each other.

although the electric field in between the plates cancel each other out, the Force on one plate from the other is

$$F = \frac {\sigma^2}_{2 \epsilon}$$

due to

$$\vec{\nabla} \cdot \vec{E} = 0$$
and
$$\rho = 0$$

why is the electric field $$\frac{\sigma}_{2 \epsilon}$$
when the electric field between the plates is 0?

orthovector said:
when the electric field between the plates is 0?

Each plate has the same charge stored on it, so what happens to this charge when the plates are put in contact? Think about a single and isolated charged conductor and how charge distributes itself.

Dear Orthovector:

I would like to give some non-mathematical explanation of the confusion. The two plates carry the kind of charge, and no doubt they will repel each other, and the force is as you put it.

Moreover, because the two plates are exactly symmetric to each other, electrically and geometrically, and properly arranged. Hence, at any point between the two plates the fields generated via the plates are of identical magnitude and opposite direction. Hence the resultant of the field is vanishing.---This doesn't mean that the plates don't repel each other, it indeed means, if we put a test charge at any point between the plates, the resultant of static electric forces is vanishing. The vanishing field is mechanically meaningful to external charge, rather than the plates.

And as to the response and question from Buffordboy23 above, I would also like to make some comments.

Each plate has the same charges stored on it, and if the plates are put in contact, the charges will of course be re-arranged. If isolated without further influence, the charges will gather on the surface of the two plates, the sharper the surface (or the larger the curvature), the denser the charges. The plates is a equipotential body, with the surface equipotential too.

Yours,
Orthotensor and Paravector !

## What is electrical force on parallel plates?

Electrical force on parallel plates is the force exerted by electric charges on each other when they are placed on two parallel plates. This force is caused by the interaction between the electric fields of the charges.

## How is the electrical force on parallel plates calculated?

The electrical force on parallel plates can be calculated using the formula F = Eq, where F is the force, E is the electric field strength, and q is the charge on the plates. This formula assumes that the plates are parallel and the electric field is uniform.

## What factors affect the electrical force on parallel plates?

The electrical force on parallel plates is affected by the distance between the plates, the magnitude of the charges on the plates, and the dielectric constant of the material between the plates. The force increases with decreasing distance and increasing charge, and is affected by the material between the plates.

## What is the direction of the electrical force on parallel plates?

The direction of the electrical force on parallel plates depends on the charges on the plates. If the plates have equal and opposite charges, the force will be attractive, pulling the plates towards each other. If the plates have the same charge, the force will be repulsive, pushing the plates away from each other.

## How is the electrical force on parallel plates used in everyday life?

The electrical force on parallel plates is used in various applications, such as in capacitors, which store electrical energy. It is also used in electronic devices, such as speakers and microphones, to convert electrical energy into mechanical energy or vice versa. The force is also used in electrostatic precipitators, which remove particles from air or gas streams.