# Electric field inside a conductor

I have some questions about electric field inside a conductor.

In fact, if a neutral conductor is placed within a capacitor, why its electric field inside the conductor at the beginning not zero, then it is zero? Why does the field disappear?

How about if a charged conductor is placed instead of a neutral one? Is the field also zero?

The argument for a perfect conductor not being able to sustain an internal field is that the perfect conductor exhibits a sea of free electrons. So any internal field that is induced in the perfect conductor quickly rearranges the electrons to cancel the internal field. It's essentially screening effects.

Actually not quite understand =.=

I also see in another post that:
"If the charges are uniformally distributed on the outer surface of the sphere, then this results in the electric field inside the sphere being zero."

I wonder why?

If you draw electric field lines for each of those charges, you would see that the combined effect would be for each of those field lines to cancel each other.

A gravitational analogue as a hollow sphere, i.e. a ping-pong ball. The gravitational field due to the ping-pong ball is uniformly zero inside the ball for the same reason.

Is it mean that if the charge is static, then the E-field = 0?

And about the electrical field lines, if I draw the diagram,
i) for the capacitor, from left to right
ii) inside the conductor, from right to left
Is it mean that the two lines cancel out each other?

Thx

I'm sorry, I'm not quite understanding you. Is this what you are asking, "what if we place a conductor in an electric field?"

Same idea holds, in a perfect conductor, the internal field will sum to zero due to screening.

I think it will be more helpful to explain with simpler English and using pictures.

A field. Positive plate on the left, negative on the right, field arrows in the middle:

+ ---> -
+ ---> -
+ ---> -
+ ---> -
+ ---> -

Now we place a conductor inside. The conductor is represented by | | in the middle:

+ --> | --> | --> -
+ --> | --> | --> -
+ --> | --> | --> -
+ --> | --> | --> -
+ --> | --> | --> -

BUT in a conductor, the electrons (negative charges) around the atoms are free to move! If an electron moves away from its usual atom, the atom becomes positively charged (because it is missing an electron).

Electrons are negatively charged, so they move in the opposite direction from an electric field. This means all the electrons move against the arrows. And there are positively charged atoms where the electrons leave from:

+ --> |- +| --> -
+ --> |- +| --> -
+ --> |- +| --> -
+ --> |- +| --> -
+ --> |- +| --> -

You see, now there is no field inside the conductor, because the electrons from one side moved to the other side. The electrons and positive atoms are charges, so they make a field too. The field of the electrons and positive atoms is the opposite of the other field, so together they make zero.

A field makes electrons move if they can move. In a conductor, they can move. So electrons will keep moving until there is no field left in the conductor.

I think it will be more helpful to explain with simpler English and using pictures.

A field. Positive plate on the left, negative on the right, field arrows in the middle:

+ ---> -
+ ---> -
+ ---> -
+ ---> -
+ ---> -

Now we place a conductor inside. The conductor is represented by | | in the middle:

+ --> | --> | --> -
+ --> | --> | --> -
+ --> | --> | --> -
+ --> | --> | --> -
+ --> | --> | --> -

BUT in a conductor, the electrons (negative charges) around the atoms are free to move! If an electron moves away from its usual atom, the atom becomes positively charged (because it is missing an electron).

Electrons are negatively charged, so they move in the opposite direction from an electric field. This means all the electrons move against the arrows. And there are positively charged atoms where the electrons leave from:

+ --> |- +| --> -
+ --> |- +| --> -
+ --> |- +| --> -
+ --> |- +| --> -
+ --> |- +| --> -

You see, now there is no field inside the conductor, because the electrons from one side moved to the other side. The electrons and positive atoms are charges, so they make a field too. The field of the electrons and positive atoms is the opposite of the other field, so together they make zero.

A field makes electrons move if they can move. In a conductor, they can move. So electrons will keep moving until there is no field left in the conductor.

Excellent.

The answer to the OP's first question is in fact that the final field inside the space occupied by the conductor is zero, because it is the superposition of the external electric field (caused by whatever charges the capacitor) and the internal electric field caused by the conductor's electrons rearranging their positions. The two fields are indentical and opposite just because the conductor's electrons keep shifting until the total electric field is zero.

How about if a charged conductor is placed instead of a neutral one? Is the field also zero?

Yes.

The principle is the same. The difference is that before putting the conductor inside the capacitor, the excess charges are already distributed (uniformly) close to the conductor's surface. After rearranging themselves due to the external electric field, the final result is again zero E inside the conductor's space, however the net charge is still non-zero so you will have a non-symmetric surface distribution of charges on the conductor.