Where are these directions coming from? (Electric Field)

[emhelp100]

Homework Statement

Two uniform infinite sheets of electric charge, one with charge density +o and the other with -o, intersect at right angles. Find and sketch the electric field $\vec{E}$

Homework Equations

$\vec{E} = \frac{\sigma}{2e_0}$

The Attempt at a Solution

Given solution:

[/B]
Numbered counterclockwise starting from $\hat{x}$

Can someone explain where the directions are coming from?
Why is it $(\frac{\hat{x}-\hat{y}}{\sqrt{2}} + \frac{-\hat{x}-\hat{y}}{\sqrt{2}})$ for 1. and etc?

 

[Merlin3189]

I don't know about electric fields, but the expressions are the sum of two vectors perpendicular to the sheets.

I guess the field due to a plane must be perpendicular to the plane, so the field between two planes is the sum of two fields.

 

[Orodruin]

Are you familiar with what the electric field from a single infinite uniformly charged plane is?

 

[emhelp100]

Are you familiar with what the electric field from a single infinite uniformly charged plane is?

no

 

[emhelp100]

I don't know about electric fields, but the expressions are the sum of two vectors perpendicular to the sheets.
View attachment 224297
I guess the field due to a plane must be perpendicular to the plane, so the field between two planes is the sum of two fields.

Why is the red line +x-y?

 

[Merlin3189]

EDIT: Ooops! Ignore this line! (I take it you mean the left hand arrow: it is perpendicular to the + plane and pointing away from it.)

You get the red vectors by adding two black vectors.
eg. the down left red arrow is what you get if you follow the black down arrow (-y) then the black left arrow (-x)

When you need to know the size of the arrows (or the magnitude of the vectors) then you CAN just look at the geometry. x and y are at 90° and equal in size (what we can call unit vectors) so the red one is √2 long. (Pythagoras, 1² + 1² = (√2)² )

 

[Merlin3189]

no

Perhaps you should take a look into this and related ideas. Hyperphysics is probably as good a place to start as any.

 

[Orodruin]

no

Then I suggest that you try to find that out first. Without that, all the talk of vector addition of both contributions will be useless. See, for example, the Khan academy video on this subject.