# Potential of two infinite lines of charge

• wakko101
In summary, the question asks for the electrical potential at all points in space for a system of two infinitely long line charges with uniform charge densities, located parallel to the x-axis at y = + and - a. To solve this, Gauss's law can be used to find the electric field of a single line charge, which can then be added together for both line charges. The difficulty lies in compensating for the fact that the lines of charge do not run along the x-axis, so the equation involving the integral of lambda over curly r needs to be adjusted accordingly.
wakko101
This is the question I have: consider the system formed by two infinitely long line charges located in the xy plane running parallel to the x-axis at y = + and - a and carrying uniform charge densities + and - lambda respectively. Find the elctrical potential at all points in space using the origin as your referenc point.

Because the lines of charge do not run along the x axis, I assume that I'm going to have to use curly r in my answer (ie. r minus r prime). So, assuming I use the equation that involves the integral of lambda over curly r, integrated over r prime, how do I rewrite curly r so that I can integrate properly?

W. =)

Use Gauss's law to get the E field of a single line charge.
Then, just add the E's from each line charge.

I'm looking for potential, not the electric field.

Also, because the lines of charge run parallel to the x axis, not along it, then r doesn't originate at the x axis, so I'll need to figure out how to compensate for that (which is what I'm having difficulty with).

## What is the concept of potential in the context of two infinite lines of charge?

In the context of two infinite lines of charge, potential refers to the amount of electrical energy per unit charge at a given point between the two lines. It is a measure of the work done in moving a unit positive charge from infinity to that point.

## How is the potential between two infinite lines of charge calculated?

The potential between two infinite lines of charge is calculated using the formula V = (λ/2πε0)ln(r2/r1), where λ is the charge density of the lines, ε0 is the permittivity of free space, and r1 and r2 are the distances from the point to the lines.

## What is the effect of increasing the distance between the two lines of charge on the potential?

Increasing the distance between the two lines of charge decreases the potential at any given point between them. This is because the electric field strength between the lines decreases as the distance between them increases, resulting in a lower potential.

## What is the relationship between potential and the direction of the electric field between two infinite lines of charge?

The direction of the electric field between two infinite lines of charge is perpendicular to the lines and points from the positive to the negative line. The potential decreases in the direction of the electric field, meaning that the potential is lower at points closer to the negative line.

## Is the potential between two infinite lines of charge always positive?

No, the potential between two infinite lines of charge can be positive or negative depending on the position of the point relative to the lines. It is positive when the point is between the lines and negative when the point is outside the lines.

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