# Finding the magnitude of a point inside 2 oppositely-charged uniform lines

## Homework Statement

Charged-line 1 (parallel to x-axis, lying on y=0m) has a charge per unit length of 4.66 microC/m.
Charged-line 2 (parallel to line 1, lying on y=.414m) has a charge per unit length of -2.5 microC/m.

Question: What is the magnitude of the net electric field at a point .202m on y-axis?

## Homework Equations

I've got the formula E=sigma/epsilon-zero, but have not used it in an application yet. Very confused as to what to do.
Does the point being at .202m on y-axis have any relevance other than that it is INBETWEEN the two charged lines? Is the ".202m" arbitrary?

## The Attempt at a Solution

I did (4.66 x 10^-6)/epsilon zero + (-2.5 x 10^-6)/epsilon zero and got a wrong answer. This stuff is very confusing to me and any help would be amazing.

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You need to find the electric field vector of each line separately, then add them together. If the line charges are of infinite length, then there's a formula that describes the magnitude of the electric field at any point a distance r away from the line charge. You probably have a textbook with it in it. If not, the formula can probably be found online.
The direction of the electric field vector is away from a positive line charge, and towards a negative one. In this problem, since there's a positive charge on one side of the point and a negative charge on the other side, the two field vectors should add and the resulting vector should point towards the negative line charge.

I hope I haven't given too much of it away...

Last edited:
Defennder
Homework Helper

## Homework Statement

Charged-line 1 (parallel to x-axis, lying on y=0m) has a charge per unit length of 4.66 microC/m.
Charged-line 2 (parallel to line 1, lying on y=.414m) has a charge per unit length of -2.5 microC/m.

Question: What is the magnitude of the net electric field at a point .202m on y-axis?

## Homework Equations

I've got the formula E=sigma/epsilon-zero, but have not used it in an application yet. Very confused as to what to do.
Does the point being at .202m on y-axis have any relevance other than that it is INBETWEEN the two charged lines? Is the ".202m" arbitrary?

## The Attempt at a Solution

I did (4.66 x 10^-6)/epsilon zero + (-2.5 x 10^-6)/epsilon zero and got a wrong answer. This stuff is very confusing to me and any help would be amazing.
Your formula for an infinite line of charge (assuming it's infinite) isn't correct to begin with. You can derive it easily from Gauss law. There's supposed to be factor of r (radial distance from line of charge somewhere inside).