# Electric field between two capacitor plates (proof)

• Harry17
In summary, the conversation is about a dipole field and how to test for uniformity. The person speaking is correcting themselves about adding two vector magnitudes and the other person confirms that adding is correct. They also mention that the field should be a dipole field and suggest testing with a specific value for d when A=5. This solution was successful in achieving uniformity.
Harry17
Homework Statement
I’m trying to prove that the electric field strength between 2 capacitor plates is uniform. To do this, I first considered a capacitor consisting of 2 circular disks, with charges +Q and -Q respectively, and determined a charge per unit area, and used that to find the charge on concentric rings going outwards from the centre of the plate. Taking the integral of the force from each ring as a function of x (the distance from the centre of the plate) and r (the distance from one of the plates) gives an integral which I am not yet able to integrate but subbing values in and using a calculator to give me a value shows that it does depend on r, when it should not.

Not sure where I’ve gone wrong, a photo of my working is attached. Any advice or solutions would be greatly appreciated.

Many thanks
Relevant Equations
F=Qq(Kd^2)
See attached image

#### Attachments

• image.jpg
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The glare makes your expressions hard to read. Am I right if I suspect you are adding two vector magnitudes when you should be subtracting them ?

The forces act in the same direction so I assumed that I add them? The two terms come from the forces from the left hand side plate and the right hand side plate

Anyway, the field should be a dipole field for ##A\downarrow 0##. Uniformity can only be expected when away from the rim (outer edge), ##d\ll A##.
So test with e.g. ##d\approx 1## when ##A=5##.

Harry17
That works now, thanks very much

## 1. What is an electric field between two capacitor plates?

The electric field between two capacitor plates is a region in space where an electric force is exerted on charged particles. It is created by the presence of two parallel plates, one positively charged and one negatively charged, and is strongest near the plates.

## 2. How is the electric field between two capacitor plates calculated?

The electric field between two capacitor plates can be calculated using the equation E = V/d, where E is the electric field strength, V is the potential difference between the plates, and d is the distance between the plates.

## 3. What factors affect the electric field between two capacitor plates?

The electric field strength between two capacitor plates is affected by several factors, including the distance between the plates, the magnitude of the charges on the plates, and the dielectric constant of the material between the plates.

## 4. How does the electric field between two capacitor plates change when the distance between the plates is increased?

As the distance between the plates is increased, the electric field strength between the plates decreases. This is because the electric force is spread out over a larger area, resulting in a weaker field.

## 5. What is the significance of the electric field between two capacitor plates?

The electric field between two capacitor plates is important in many practical applications, such as in electronic devices and circuits. It also plays a crucial role in understanding the behavior of charged particles and electromagnetic waves.

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