Is the Electric Field Inside an Irregular Shaped Conductor Always Zero?

[sanoo]

In an irregular shaped charged conductor will the electric field E at all points within the conductor be zero? If yes, then how?

 

[Barloud]

I assume you are talking about a purely static situation.
Without external electric field, the net electric charge in each point of the conductor is zero (lets keep it simple: I assume there are no excess charges in the conductor).
Under the action of an external field, the positive and negative charges in the conductor displaces, so that the net electric charge in each point of the conductor (local charge) is not zero. If you sum the charge of all these points over the whole volume (global charge), it will however remains equal to zero.
The local charges are so smart that they arrange themselves so that the field is zero in the whole conductor. It is however a very difficult task to compute the local distribution for complex geometries.

 

[sanoo]

Thanks for the reply. But if a conductor is charged, the charges are spread on its surface. Will not those charges impose an electric field within the conductor? Will the local charges again arrange themselves to cancel the field produced?

 

[vanhees71]

The trick is that the charges are distributed over the surface precisely such that there is no electric field inside the conductor. This is only true for the static case!

 

[sardar]

The electric field within a conductor is directly related to the distribution of charges on its surface. In an irregular shaped conductor, the charges will be distributed unevenly, resulting in a non-uniform electric field within the conductor. Therefore, it is not possible for the electric field to be zero at all points within the conductor.

However, in the case of a perfectly spherical conductor with a uniform charge distribution, the electric field within the conductor will be zero at all points. This is because the charges on the surface of the conductor will cancel out the electric field inside, resulting in a net zero electric field.

In general, the electric field within a conductor will be strongest near sharp edges or points, where the charge density is highest. This is known as the "corona effect" and is often observed in high voltage systems.

It is important to note that the electric field within a conductor is a dynamic quantity and can change depending on the external factors such as the magnitude and distribution of charges, as well as the surrounding environment. Therefore, it is not always possible to predict the exact value of the electric field at a specific point within an irregular shaped conductor.