Find the electric field everywhere resulting from two infinite planes

In summary, the electric fields of the positive and negative points charges in this situation cancel each other out.
  • #1
annamal
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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
Screen Shot 2022-04-20 at 6.24.23 PM.png
 
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  • #2
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.

1650499099191.png


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?
 
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  • #3
Look at the field for each infinite plane separately first.
 
  • #4
annamal said:
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.
 
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  • #5
They cancel out in the space outside the two plates, but in the space in between the two plates they amplify each other.
 

FAQ: Find the electric field everywhere resulting from two infinite planes

What is the concept behind finding the electric field resulting from two infinite planes?

The concept behind finding the electric field resulting from two infinite planes is based on the principle of superposition. According to this principle, the total electric field at a point is the sum of the individual electric fields created by each source charge.

What are the key equations used to calculate the electric field resulting from two infinite planes?

The key equations used to calculate the electric field resulting from two infinite planes are Gauss's Law and Coulomb's Law. Gauss's Law states that the electric flux through a closed surface is proportional to the enclosed charge, while Coulomb's Law describes the force between two point charges.

How does the distance between the two infinite planes affect the electric field?

The distance between the two infinite planes has a direct impact on the strength of the electric field. As the distance increases, the electric field decreases. This is because the electric field is inversely proportional to the distance squared according to Coulomb's Law.

What is the direction of the electric field resulting from two infinite planes?

The direction of the electric field resulting from two infinite planes is perpendicular to the planes and points away from the positively charged plane and towards the negatively charged plane. This is because the electric field lines always point from positive charges to negative charges.

Can the electric field resulting from two infinite planes be negative?

Yes, the electric field resulting from two infinite planes can be negative. This occurs when the two planes have opposite charges, with the positively charged plane having a greater magnitude of charge. In this case, the electric field will be directed towards the negatively charged plane, resulting in a negative value.

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