# Non-uniformly charged disc

• Hatyk
In summary, the problem is to find the total charge of a disk with radius R, where one half has a charge density of +2σ and the other half has a charge density of -σ. The proposed solution is to split the disk in the middle and find the total charge of each half separately, although there is some ambiguity in the statement of the problem.

## Homework Statement

I have a disc with radius R. One half has the charge density of +2σ and the other half has −σ. The task is to find the total charge of the disc.

## Homework Equations

dQ=ρ2πr^2 I would use this equation if the charge density was uniform

## The Attempt at a Solution

My first idea was to split the disc in the middle and find the total charge of each part separately and then add them up. Thinking about it now, this solution feels wrong. What is the correct solution?

Well, in my opinion the statement of problem not say if the half is the half of radius or the half of surface. My intuition says the half of surface, but you can make the two cases

Statement of the problem is not complete. Which two halves are we talking about?

Hatyk said:

## Homework Statement

I have a disc with radius R. One half has the charge density of +2σ and the other half has −σ. The task is to find the total charge of the disc.

## Homework Equations

dQ=ρ2πr^2 I would use this equation if the charge density was uniform

## The Attempt at a Solution

My first idea was to split the disc in the middle and find the total charge of each part separately and then add them up. Thinking about it now, this solution feels wrong. What is the correct solution?
I see nothing wrong with your assumption. I'll go on a limb and say it doesn't matter if the charges are all +2s on one side and -s on the obverse side, vs. each side has half +2s and the other half -s.

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How about half the radius with +2σ and the other half with -σ?

Chandra Prayaga said:
How about half the radius with +2σ and the other half with -σ?
Personally I'd have some difficulty justifying that given how the area of a disk varies with the radius

rude man

## 1. What is a non-uniformly charged disc?

A non-uniformly charged disc refers to a circular object that has an uneven distribution of positive or negative charges on its surface. This means that the charges are not equally spaced or distributed on the disc, resulting in a non-uniform electric field.

## 2. How is the electric field calculated for a non-uniformly charged disc?

The electric field for a non-uniformly charged disc can be calculated using the superposition principle, where the electric field is determined by adding the contributions of each individual charge on the disc. This can be done using integration or by breaking up the disc into smaller uniform sections and calculating the electric field for each section.

## 3. What is the difference between a uniformly charged disc and a non-uniformly charged disc?

In a uniformly charged disc, the charges are evenly distributed on the surface, resulting in a uniform electric field. On the other hand, in a non-uniformly charged disc, the charges are unevenly distributed, resulting in a non-uniform electric field.

## 4. How does the electric field vary with distance from a non-uniformly charged disc?

The electric field from a non-uniformly charged disc will vary with distance from the disc. At points close to the disc, the electric field will be stronger due to the uneven distribution of charges. As the distance increases, the electric field will decrease and eventually become uniform at a certain distance from the disc, depending on the charge distribution.

## 5. What are some real-world applications of non-uniformly charged discs?

Non-uniformly charged discs are commonly used in various electronic devices such as capacitors and disk drives. They are also used in particle accelerators to create non-uniform electric fields for accelerating particles. Non-uniformly charged discs also play a role in the study of planetary magnetic fields and in the design of certain types of batteries.