# How Should I Integrate Electric Potential for Oppositely Charged Parallel Lines?

• wakko101
In summary, the conversation discusses the calculation of electric potential using infinite lines of charge and a reference point at the origin. The integration of the electric field from the lines results in a natural logarithm, causing difficulty in the calculation for one of the lines. The issue is resolved by using the absolute value of the distance to the line instead of just the distance.
wakko101
electric potential...again.

So, I've still got my two infinite lines of charge that run parallel to the x-axis running along the lines x = a and x = -a and with charge density + and - lambda respectively.

I've figured out that using the origin as my reference point allows me to integrate the electric field of my lines from a to the point in question (r). However, because the field goes like 1/r, we end up with a ln of something in the potential. For the line that's positive a away from the x axis, there's no problem. But, for the line that runs along x = -a, how can I integrate? should I be integrating from a to r again, or from -a to r. The problem with the latter is that you can't have the natural logarithm of a negative number.

I would REALLY appreciate any advice. I'm a little desperate...

Cheers,
W. =)

Remember, the r in 1/r is the distance to the charge so it should always be positive. If your point is (x, y) then the distance to the line x = -a is |x + a| and the distance to the line x=a is |x-a|

that makes sense...I figured it was a that I needed to use, but I just wanted to be sure.

Thanks for the help. =)

## What is electric potential?

Electric potential is the amount of electric potential energy per unit of charge at a given point in an electric field. It is a measure of the work required to move a unit positive charge from a reference point to a specific point against an electric field.

## How is electric potential different from electric potential energy?

While electric potential is a measure of the electric potential energy per unit of charge, electric potential energy is the potential energy a charged particle possesses due to its position in an electric field. In other words, electric potential energy is the potential to do work, while electric potential is the amount of potential energy per unit of charge.

## What is the unit of electric potential?

The unit of electric potential is volts (V). This unit is equivalent to joules per coulomb (J/C) in the SI system of units.

## How is electric potential measured?

Electric potential is measured using a voltmeter, which measures the difference in electric potential between two points in an electric field. The voltmeter is connected in parallel to the points of interest and measures the voltage difference between them.

## Can electric potential be negative?

Yes, electric potential can be negative. This indicates that the direction of the electric field is opposite to the direction of the movement of a positive test charge. A negative electric potential does not necessarily mean a negative electric potential energy, as the energy depends on the charge of the test particle.

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