# Electric field inside hollow conductor with a charge

• Tiago3434
In summary, the conversation discusses the concept of Gauss' Law and the behavior of charges in a hollow conductor with an internal point charge. It is stated that in electrostatic equilibrium, the charges rearrange themselves to cancel the electric field inside the conductor. However, it is also noted that this does not occur in the cavity where the point charge is located. This is because the charge density needed to cancel out the electric field from the point charge cannot be arranged in a spherical shell. Additionally, it is mentioned that charges are not affected by the electric field they produce and are constrained to move only inside the conductor.
Tiago3434
Ok, this might be a really dumb question, but I still am asking it: I was reading about gauss' Law when it comes to a hollow conductor with a (say) point charge inside it, and it seems intuitive to me that, in electrostatic equilibrium, the charges rearrange themselves to cancel the electric field inside it, after all, if there were a nonzero electric field, there would be acceleration, which violates the idea that the system is in electrostatic equilibrium. Here is the q: is there a reason (or intuition, perhaps) as to why the charges don't rearrange themselves to cancel all electric field inside it, including inside the cavity, where the point charge lies?

For this to happen, you would need a charge density in the shell which produces an electric field inside the shell with the form ##-kq/r^{2}\;\hat{r}## to cancel out the electric field from the point charge. However, there is no arrangement of charge density in a spherical shell which can produce such an electric field inside the shell.

Tiago3434 said:
...after all, if there were a nonzero electric field, there would be acceleration, which violates the idea that the system is in electrostatic equilibrium.

A charge is not affected by the electric field that it produces, so no acceleration.

The charges can't go just anywhere. By definition of a "hollow" conductor, they are constrained to move only inside the conductor. If not, they would move to the place where you placed your internal charge and cancel it out.

## 1. What is an electric field inside a hollow conductor?

An electric field inside a hollow conductor is the force per unit charge experienced by a charged particle inside the conductor. It is created by the presence of a charge on the surface of the conductor.

## 2. How is the electric field inside a hollow conductor different from the electric field outside?

The electric field inside a hollow conductor is zero, while the electric field outside is non-zero. This is because the charges on the surface of the conductor create an equal and opposite electric field inside that cancels out the external electric field.

## 3. What happens to the electric field inside a hollow conductor if the charge on the surface changes?

If the charge on the surface of the hollow conductor changes, the electric field inside will also change. The electric field inside is directly proportional to the surface charge density, so an increase in charge will result in an increase in the electric field strength inside the conductor.

## 4. Can the electric field inside a hollow conductor ever be non-zero?

No, the electric field inside a hollow conductor will always be zero. This is due to the principle of electrostatic equilibrium, where the electric field inside a conductor must be zero in order for charges to remain at rest.

## 5. How can the electric field inside a hollow conductor be calculated?

The electric field inside a hollow conductor can be calculated using the formula E = σ/ε0, where σ is the surface charge density and ε0 is the permittivity of free space. Alternatively, it can also be calculated using Gauss's law, which states that the electric field inside a hollow conductor is equal to the charge enclosed divided by the surface area of the conductor.

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