Is the Electric Field Zero Inside Any Shape of an Empty Cavity in a Conductor?

In summary, the electric field inside an empty cavity in a conductor is zero regardless of the shape of the cavity. This is because, in a conductor, the electrons and protons tend to create fields that cancel each other out. Since the cavity is empty, there is no net charge density and any charge would only be on the surface of the cavity. This means that a Gaussian surface around the cavity inside the conductor would not contain any charge and thus have a zero electric field.
  • #1
hisashiburi
2
0

Homework Statement


The electric field inside an empty cavity in a conductor is zero. Is this statement true no matter what the shape of the cavity? Why or why not?


Homework Equations


Electric field equation. E = kQ / R^2


The Attempt at a Solution


I can't seem to figure out if this is true no matter what the shape.
 
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  • #2
no, consider a charge in a cavity in a conductor.

it's only in the meat of the conductor, because when you would put a conductor in a field, the electrons would move and create a field with the protons on their own. The two fields tend to cancel. But in a hole, you don't have this problem. (The edges of the conductor will be charged however, in that case.)
 
  • #3
jacobrhcp said:
no, consider a charge in a cavity in a conductor.

it's only in the meat of the conductor, because when you would put a conductor in a field, the electrons would move and create a field with the protons on their own. The two fields tend to cancel. But in a hole, you don't have this problem. (The edges of the conductor will be charged however, in that case.)

That's correct, but it's stated that the cavity is empty, so it doesn't contain a charge. There's no net charge density in the conductor and the cavity is empty, so the only place a charge could be is on the surface of the cavity. Now consider a gaussian surface around the cavity but inside the conductor.
 
  • #4
oh I'm sorry, ah well... I guess Dick gave you quite a hint there.
 

FAQ: Is the Electric Field Zero Inside Any Shape of an Empty Cavity in a Conductor?

What is an electric field in an empty cavity?

An electric field in an empty cavity refers to the electric field present inside a cavity or hollow space that is completely devoid of any material objects. This is usually studied in the context of electromagnetic theory and can be calculated using Maxwell's equations.

How is an electric field in an empty cavity different from a regular electric field?

An electric field in an empty cavity differs from a regular electric field in the sense that it exists in a space with no material objects. In a regular electric field, the field lines are influenced by the presence of charges and materials, whereas in an empty cavity, the field lines are solely determined by the boundary conditions of the cavity.

What factors affect the strength of an electric field in an empty cavity?

The strength of an electric field in an empty cavity is affected by several factors, including the size and shape of the cavity, the boundary conditions of the cavity, and the distribution of charges outside the cavity. These factors determine the direction and magnitude of the electric field inside the cavity.

Can an electric field exist in an empty cavity with no charges present?

Yes, an electric field can exist in an empty cavity even when there are no charges present. This is because the boundary conditions of the cavity can create an electric field, which is independent of the presence of charges. However, the strength and direction of the electric field will be affected by the distribution of charges outside the cavity.

How is the electric field in an empty cavity used in practical applications?

The electric field in an empty cavity has various practical applications, including in the design of microwave cavities for communication systems, in the study of quantum electrodynamics, and in particle accelerators. It is also used in the development of cavity resonators for high-frequency applications such as radio astronomy and particle physics experiments.

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