# Calculus with the electric field

• pakman2012

## Homework Statement

1. Find the electric field at point P for a line segment with length L. Diagram attached.

## Homework Equations

attached equations

## The Attempt at a Solution

I have next to no clue on how to do this question. My first idea was to try and set up one of the lengths as r, and work from there, but I wasn't able to do anything conclusively. The most confusing part is not being able to do the calculus and relating the variables to fit the purposes of the problem. How exactly do you find the potential of something like this, in general?

Any help for this question will be greatly appreciated.

#### Attachments

• Diagram 1.bmp
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• Equations 1.bmp
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Last edited:
First pick appropriate coordinate axes. The line along the x-axis and the left end at the origin for example.
Then consider the contribution to E resulting from a small line element dx (with charge density lambda say) and add up (integrate) all the contributions.

First pick appropriate coordinate axes. The line along the x-axis and the left end at the origin for example.
Then consider the contribution to E resulting from a small line element dx (with charge density lambda say) and add up (integrate) all the contributions.

The trick is to use sine to relate the small section of conductor(dx) to the distance from your point.