What is the Electric Field at the Origin Due to Two Point Charges?

[negatifzeo]

Homework Statement

A +8·µC charge is located at coordinates (3,5)·m, and a -2·µC charge is located at coordinates (3,-2)·m. Find the electric field at the origin.
E= ? V/m x + ? V/m y

(It asks for the solution in x and y components)

Homework Equations

I was using E=kq/r^2, where E is the electric field vector (Away if positive, towards if negative) K was 9x10^9, q is the value of the charge.

The Attempt at a Solution

First I used pythagorean theorem to determine distance to origin. Then I used this value for r.
Using the formula for the +8 charge I get E=2117.61 and for the -2 charge I got E=1376.63. Then I used the trig functions from the triangles to solve for the components, which I thern added together for the wrong answer. Where have I gone wrong here?

 

[bob1182006]

-2 charge, E=1376.63, it should be negative, or pointing into the right so when you add the 2 E vectors you will be subtracting them.

I get the same values for E's, just that negative sign, Hope that's the problem!

 

[negatifzeo]

The angles from the original triangles are used to calculate the components, correct? I was treating the +8 charge as my negative vector as electric fields point outwards from positive charges, right?

 

[bob1182006]

Yes,

I think if you use the 8 charge as the negative, you will get the wrong answer, maybe just -1*answer wil fix it but I'm not 100% sure on that.

You should find the 2 vector pointing away, then inverse it so it points inward and then find the x-y components and subtract or add the components.

Also for your -2 charge, I got E=1384.62 not 1376.63

 

[alphysicist]

Hi negatifzeo,

Homework Statement

A +8·µC charge is located at coordinates (3,5)·m, and a -2·µC charge is located at coordinates (3,-2)·m. Find the electric field at the origin.
E= ? V/m x + ? V/m y

(It asks for the solution in x and y components)

Homework Equations

I was using E=kq/r^2, where E is the electric field vector (Away if positive, towards if negative) K was 9x10^9, q is the value of the charge.

The Attempt at a Solution

First I used pythagorean theorem to determine distance to origin. Then I used this value for r.
Using the formula for the +8 charge I get E=2117.61 and for the -2 charge I got E=1376.63. Then I used the trig functions from the triangles to solve for the components, which I thern added together for the wrong answer. Where have I gone wrong here?

What components and wrong answer did you get?

 

[negatifzeo]

I finally got the correct answer, my problem was rounding a bit too much.