Where are these directions coming from? (Electric Field)

AI Thread Summary
The discussion focuses on understanding the electric field generated by two infinite sheets of charge, one positively charged and the other negatively charged. Participants clarify that the electric field from a plane is always perpendicular to the plane, and the total field between the sheets results from the vector sum of the individual fields. The expressions for the electric field directions are derived from vector addition, with emphasis on the geometry involved in calculating magnitudes. Suggestions for further learning include resources like Hyperphysics and Khan Academy to grasp the underlying concepts better. Understanding the electric field from a single charged plane is crucial for comprehending the overall field configuration.
emhelp100
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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}

upload_2018-4-18_23-55-24.png

Homework Equations


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

The Attempt at a Solution


Given solution:
upload_2018-4-18_23-56-21.png

[/B]
Numbered counterclockwise starting from \hat{x}
upload_2018-4-18_23-57-42.png

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?
 

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

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.
 

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Are you familiar with what the electric field from a single infinite uniformly charged plane is?
 
Orodruin said:
Are you familiar with what the electric field from a single infinite uniformly charged plane is?
no
 
Merlin3189 said:
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?
 
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.)
ElectricFieldX3.png

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 )
 

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Last edited:
emhelp100 said:
no
Perhaps you should take a look into this and related ideas. Hyperphysics is probably as good a place to start as any.
 
emhelp100 said:
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.
 
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