Find the electric field everywhere resulting from two infinite planes

[annamal]

Homework Statement

Find the electric field everywhere resulting from two infinite planes with equal but opposite charge densities

Relevant Equations

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

What I don't understand is how come the electric field of the negative plane isn't pointing towards the positive plane (in blue) and cancelling out the electric field of the positive plane (in red). See image

 

[TSny]

Recall the electric field patterns of positive and negative point charges as shown here. In particular, note the directions of the fields.

Suppose we have a positive and a negative point charge positioned as shown below.

Consider the direction of the electric field at point p due to the positive charge alone.
Then consider the direction of the electric field at point p due to the negative charge alone.
Does the field of the negative charge tend to cancel the field of the positive charge at point p?

 

[bob012345]

Look at the field for each infinite plane separately first.

 

[kuruman]

What I don't understand is how come the electric field of the negative plane isn't pointing towards the positive plane (in blue) and cancelling out the electric field of the positive plane (in red).

Electric field lines originate at positive charges and stop at negative charges. That follows from Gauss's law. You can draw the blue lines if you wish, but you have to be careful. Remember that the electric field points in the direction of the force on a positive test charge. A positive test charge placed between the plates will experience a repulsive force from the positive charges on the left and an attractive force from the negative charges on the right. So if you draw blue lines representing the electric field from the negative charges, they should point left to right, same as the red lines. In that case you might as well draw one set of lines and be done with it.

 

[Delta2]

They cancel out in the space outside the two plates, but in the space in between the two plates they amplify each other.