# The work required for adding a charge to an infinite charge distribution

• Deeviance
In summary, the problem involves finding the energy required to add an additional charge to an infinite equidistant linear charge distribution, where the charges are brought from an infinite distance to their spot in the distribution. The solution involves using potential and the work being equal to q V, where V is an infinite sum of alternating signs with terms like 1/n.
Deeviance

## Homework Statement

Find the energy required to add an additional charge to the chain
in the limit where the total number of charges approaches infinity.

So, I have a equidistant linear charge distribution like + - + - + -... where the total number of charges approaches infinity. The charges are being brought from an infinite distance to there spot in the charge distribution.

What is the energy required to add a charge on to the "end" of it?

## Homework Equations

Electric force = k(Q1Q2)/d^2
work = Integral of (Fdot Dr) from path begin to path end

## The Attempt at a Solution

I wish I could more here, but its one of these problems that I can't set up, so I can't really give an attempted solution but here are my thoughts.

(backed up by nothing but my intuition)

It will be a finite number as most of the force due to charge distribution will cancel out.

It will be close to the amount of energy required to add a charge to a single charge distribution because of the cancellation.
Any direction would be much appreciate.

Last edited:
Use potential. The work equals q V.
V is an infinite sum of alternating sign with terms like 1/n.

## 1. What is an infinite charge distribution?

An infinite charge distribution is a theoretical concept in physics that describes a system with an infinite number of charges spread out over an infinite space. This distribution is often used in calculations and models to simplify complex systems that involve a large number of charges.

## 2. What is meant by the "work required" for adding a charge to an infinite charge distribution?

The "work required" refers to the amount of energy needed to add a new charge to an existing infinite charge distribution. This energy is required because the charge will interact with the existing charges in the distribution, causing a change in the electric field and potential energy of the system.

## 3. How is the work required for adding a charge to an infinite charge distribution calculated?

The work required for adding a charge to an infinite charge distribution can be calculated using the formula W = qΦ, where W is the work required, q is the charge being added, and Φ is the potential of the infinite charge distribution at the location of the new charge. This calculation takes into account the existing electric field and potential energy of the system.

## 4. Is the work required for adding a charge to an infinite charge distribution always positive?

No, the work required can be either positive or negative depending on the charge being added and the potential of the infinite charge distribution at that location. If the new charge has the same sign as the existing charges, the work required will be positive. However, if the new charge has the opposite sign, the work required will be negative.

## 5. How does the work required for adding a charge to an infinite charge distribution relate to the concept of electric potential?

The work required is directly related to the electric potential of the infinite charge distribution. The electric potential is a measure of the potential energy per unit charge at a specific point in space. As the potential of the infinite charge distribution changes due to the addition of a new charge, the work required to add that charge also changes.

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