# Charge of a capacitor

## Main Question or Discussion Point

A capacitor have zero net charge because there is same amount of positive and negative charges. However, if amount of +ve and -ve charge are the same, shouldn't delta V and electric field strength be zero? Why is there still an electric field?

This may be silly, but it indeed confuses me a lot.

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ranger
Gold Member
Have you ever heard about Coulomb's law? Where the electric field lines starts from the positive charge and ends at the negative charge. Because of the dielectric, the charges are separated from each other and hence a stronger electric field.

+=====>=======>-
+=====>=======>-
+=====>=======>-
+=====>=======>-

+ positive charge
- negative charge
= electric field lines
> direction of electric field lines

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Imagine initially all the + and - charges are together - they attract each other - so you must apply some energy to separate them. This is called work - its equal to force times distance. The amount of work you invest in separating each positive charge from a negative charge is stored in the field -i.e., energy is conserved.

A capacitor have zero net charge because there is same amount of positive and negative charges. However, if amount of +ve and -ve charge are the same, shouldn't delta V and electric field strength be zero? Why is there still an electric field?

This may be silly, but it indeed confuses me a lot.

I will try to explain the simpliest way I can.
Imagine two metal spheres :One with diameter d1 and another one with diameter D2>d1.
Let both be hollow metal spheres and let the smaller be located inside (in the center) of the bigger one.
Now let some process shift certain amount of electons from the smaller sphere to the bigger one.
The outcome is ,and what arises in the space between two spheres ,a certain electrical field created by the separation of charges (electrons).
But ,what would you observe if you are observer in the space outside the bigger sphere ? No electrical field.
For you,the spherical metal object stays neutral,and in this part of your thinking you are right .

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I will try to explain the simpliest way I can.
Imagine two metal spheres :One with diameter d1 and another one with diameter D2>d1.
Let both be hollow metal spheres and let the smaller be located inside (in the center) of the bigger one.
Now let some process shift certain amount of electons from the smaller sphere to the bigger one.
The outcome is ,and what arises in the space between two spheres ,a certain electrical field created by the separation of charges (electrons).
But ,what would you observe if you are observer in the space outside the bigger sphere ? No electrical field.
For you,the spherical metal object stays neutral,and in this part of your thinking you are right .
So the entire sphere maintains the same charge (let's say neutral), it is just transferred from the inner sphere to the outer surface sphere. So outside of the sphere you see no Electric Field but inside there is one between the outer and inner spheres.
It's confusing for me because I see a capacitor as kind of similar to a dipole, but whereas a dipole has an electric field which decreases ~$$\frac{1}{r^3}$$, but in a capacitor there is no E outside.
Can sombody explain why the capacitor shouldn't be thought of as just a big dipole?

Look into Gauss law

A capacitor have zero net charge because there is same amount of positive and negative charges. However, if amount of +ve and -ve charge are the same, shouldn't delta V and electric field strength be zero? Why is there still an electric field?

This may be silly, but it indeed confuses me a lot.
I hope that you are talking about electric field within the two plates of the capacitor.

First you must understand that the mere presence of equal and opposite charges i.e., zero net charge, is no condition for a region to have zero electric field.

Let us now assume a parallel plate capacitor for simplicity. Let the left plate be positively charged and the right plate be negatively charged. The field at any point between the plates because of the positively charged plate is directed towards the right. The field at any point between the plates because of the negatively charged plate is also directed towards the right. Hence, the fields only add and DO NO CANCEL.

To determine the direction and magnitude of the electric field within a capacitor kindly use Gauss law. Try applying Gauss law to determine field at a point just outside a conducting sheet of charge having a uniform charge distribution. Begin by considering a cylindrical Gaussian surface.

This would be covered in just about any school/under graduate level text book in electricity and magnetism.

I hope that helps.

So the entire sphere maintains the same charge (let's say neutral), it is just transferred from the inner sphere to the outer surface sphere. So outside of the sphere you see no Electric Field but inside there is one between the outer and inner spheres.
It's confusing for me because I see a capacitor as kind of similar to a dipole, but whereas a dipole has an electric field which decreases ~$$\frac{1}{r^3}$$, but in a capacitor there is no E outside.
It's not true that for every capacitor $E_{outside}=0$ !!
Only for self-closing geometries ,like in example of 2 spheres I described ,this field equals 0.
Therefore,you have a geometry dependent situation which vary from case to case (assuming $Q_{net}=0$)

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So in a parralel plate capacitor with finite plates is there an E outside?

ranger
Gold Member
So in a parralel plate capacitor with finite plates is there an E outside?
When two parallel plates [+ and -], are placed next to each other, the electric fields inside add, while outside cancels out.

So in a parralel plate capacitor with finite plates is there an E outside?
Yes, there is. It decreases approximately with 1/r^3.

Am I misunderstanding something, or are the last two responses contradictory? Do the fields cancel (I assume cancel means E=0) on the outside of the plates, or do they decrease with 1/r^3.

ranger
Gold Member
Am I misunderstanding something, or are the last two responses contradictory? Do the fields cancel (I assume cancel means E=0) on the outside of the plates, or do they decrease with 1/r^3.
Mayb if you look at the math and some illustrations, it will become clear:
http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Capacitors/ParallCap.html [Broken]

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Mayb if you look at the math and some illustrations, it will become clear:
http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Capacitors/ParallCap.html [Broken]
Thanks, so with infinite sized parrallel plate capacitors Eoutside=0. and for finite sized parallel plate capacitors the E inside adds together and E outside is ~ 1/r^3 correct?

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ranger
Gold Member
Thanks, so with infinite sized parrallel plate capacitors Eoutside=0. and for finite sized parallel plate capacitors the E inside adds together and E outside is ~ 1/r^3 correct?
Hi americanforest,

I'm sorry, I ignored when you said finite plate. My case was for an ideal capacitor with infinite plates. Manchot reply is true where it decreases 1/r^3 becuase of the dipole field.

I am surprised to see so much replies!

I will try to explain the simpliest way I can.
Imagine two metal spheres :One with diameter d1 and another one with diameter D2>d1.
Let both be hollow metal spheres and let the smaller be located inside (in the center) of the bigger one.
Now let some process shift certain amount of electons from the smaller sphere to the bigger one.
The outcome is ,and what arises in the space between two spheres ,a certain electrical field created by the separation of charges (electrons).
But ,what would you observe if you are observer in the space outside the bigger sphere ? No electrical field.
For you,the spherical metal object stays neutral,and in this part of your thinking you are right .
Thank you very much for your answer. I'll try to look it at a different way

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What I described is nothing else than a "spherical capacitor".
For that and other cases see:http://ocw.mit.edu/NR/rdonlyres/Physics/8-02TSpring-2005/7EC48A5F-B4BB-485D-BF6C-91CA3D5C448C/0/presentati_w03d1.pdf [Broken]

americanforest said:
So in a parralel plate capacitor with finite plates is there an E outside?
Yes there is (usually very small though).
Only ,when the plates are infinite (or they intersect in infinity ),Eoutside=0

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