# Electric field inside a sphere

• jackyyoyoyo
In summary, the electric field inside a sphere is zero, while the electric field inside a conductor is not zero unless the conductor has a thin enough layer. If the sphere is not a conductor, the electric field inside the sphere is also zero. If the sphere is a conductor, the electric field inside the sphere is not zero unless the conductor has a thin enough layer.
jackyyoyoyo
I'm confused with the electric field inside a sphere.
The book said that E=keQr/a^3
While one of the properities of electrostatic equilibrium mentioned that the E-field is zero everywhere inside the conductor.
Are there any exceptional cases?

You'll have to tell us more about the problem: Conducting ot non-conducting sphere? What if any electrical charges are present, and where are they?

jackyyoyoyo
Are you sure that your book was describing the field within a conducting sphere?

jackyyoyoyo said:
I'm confused with the electric field inside a sphere.
The book said that E=keQr/a^3
That looks to me like the field within a uniform sphere of charge Q and radius a at a distance r from the center (where r < a). It's not a conducting sphere.

I think I lack of consideration on whether the sphere is conducting or insulating.
The conducting sphere will have E=0 while the insulating sphere will have E=keQr/a^3

jackyyoyoyo said:
I think I lack of consideration on whether the sphere is conducting or insulating.
The conducting sphere will have E=0 while the insulating sphere will have E=keQr/a^3

This is still incomplete!

You need to go back to the book, and re-read from the beginning the derivation that produced such an electric field. Pay attention to the charge distribution or charge density inside the sphere. Is it a uniform distribution? Or does it have a radial dependence, etc...?

If you still do not understand this, then copy the exact scenario from your text into here. Otherwise, we are looking at this problem through what you think you understood, not what it actually is.

Zz.

Doc Al said:
That looks to me like the field within a uniform sphere of charge Q and radius a
In case I wasn't clear: By "uniform sphere of charge Q" I mean a sphere of radius "a" filled with a uniform charge density such that the total charge is Q.

Doc Al said:
That looks to me like the field within a uniform sphere of charge Q and radius a at a distance r from the center (where r < a). It's not a conducting sphere.
Doc Al said:
In case I wasn't clear: By "uniform sphere of charge Q" I mean a sphere of radius "a" filled with a uniform charge density such that the total charge is Q.
You are right!
and the charge is uniformly distributed.

Then the sphere is not a conductor, and the following statement does not apply.
jackyyoyoyo said:
While one of the properities of electrostatic equilibrium mentioned that the E-field is zero everywhere inside the conductor.

jackyyoyoyo said:
I'm confused with the electric field inside a sphere.
The book said that E=keQr/a^3
While one of the properities of electrostatic equilibrium mentioned that the E-field is zero everywhere inside the conductor.
Are there any exceptional cases?

I think both conditions are not quite the same.

For the sphere, if you have charges distributed equally on the surface of the sphere, then the net electric field inside the sphere is zero.

For the conductor, the reason why there is no field inside a conductor is a bit different. Because a conductor has so much free electrons,
a field cannot penetrate inside a conductor. But if you have a thin enough conductor, and a strong enough field, then sure the field can
penetrate through the thin conductor and so you can have a field there.

You may have to try to visualize how a field is created. A field is created by having a net charge whether positive or negative. Supposed
you have a metal wire of your choice which obviously has net charge of zero. Although this wire has a lot of free electrons moving around but they
are balanced out by the same positive charge of the nucleus. In order to created a field within a conductor, you need to somehow
"move" the electrons at least temporarily to one side locally which exposes a net positive charges. So now you have a net charge
which will give you an electric field. But since the wire or any typical conductor has so much free electrons that as soon as you "move" a
group of electrons to one side, that empty space will immediately replaced by a bunch of free electrons from nearby since there are
so much available electrons. Think of trying to move water in a bucket with your hand. As soon as you move the water, that temporary
void will be replaced with water nearby. That is why people say there is no field within a conductor since it's very difficult to get an electric
field strong enough to penetrate a conductor. But on the surface of a conductor, a field doesn't have to be strong enough to temporarily
move electrons to create a temporary net charge.
On the other hand, if you have a non-conductor which is the opposite of conductor that there are very little free electrons, therefore
it's easier to create a net charge since there are not enough free electrons to fill the gap.

## 1. What is an electric field inside a sphere?

The electric field inside a sphere is the force per unit charge experienced by a charged particle placed inside the sphere. It is a vector quantity and is represented by the symbol E.

## 2. How is the electric field inside a sphere calculated?

The electric field inside a sphere can be calculated using the formula E = Q/4πε0r2, where Q is the charge of the sphere, ε0 is the permittivity of free space, and r is the distance from the center of the sphere to the point where the electric field is being calculated.

## 3. What is the direction of the electric field inside a sphere?

The electric field inside a sphere is always directed towards the center of the sphere. This is because the electric field lines always point in the direction of the force on a positive test charge.

## 4. How does the electric field inside a sphere vary with distance?

The electric field inside a sphere varies inversely with the square of the distance from the center of the sphere. This means that as the distance from the center increases, the electric field decreases.

## 5. Can the electric field inside a sphere be zero?

Yes, the electric field inside a sphere can be zero at the center of the sphere. This is because the electric field is defined as the force per unit charge, and at the center of the sphere, the force on a charged particle would be zero due to the symmetry of the electric field.

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