23.8
Electric Field Inside a Conductor
When a conductor is placed in an external electric field, the free charges in the conductor redistribute and very quickly reach electrostatic equilibr…
Consider a conductor placed in an external electric field. In a conductor, only the electrons are free to move.
The free electrons migrate opposite to the external electric field, accumulating at one end of the surface.
Consequently, the other end of the surface has a lesser number of electrons and so gains a net opposite surface charge, thus polarizing the conductor.
Due to the accumulation of surface charges, an internal electric field is developed opposite the external field.
As the charges continue to move, the internal field magnitude increases until it equals the external field.
The conductor now reaches a steady state known as electrostatic equilibrium, and the charges do not move anymore.
In this condition, the net field at all the points inside the conductor, which is the sum of the external and the internal fields, vanishes.
From Gauss' law, zero electric fields imply no net charge enclosed inside a conductor.
View the full transcript and gain access to JoVE Core videos
Q1: Why is the electric field zero inside a conductor at electrostatic equilibrium?
At electrostatic equilibrium, free electrons in the conductor migrate until they create an induced electric field that exactly opposes the external field. The net field inside becomes zero because the external and internal fields cancel completely. From Gauss's law, a zero electric field means no net charge is enclosed within the conductor's volume.
Q2: What happens to free electrons when a conductor is placed in an external electric field?
Free electrons migrate opposite to the external electric field direction, accumulating at one surface of the conductor. This creates a region with excess electrons and a region with fewer electrons, causing the conductor to polarize. The electron movement continues until the induced electric field balances the external field, establishing electrostatic equilibrium.
Q3: How does conductor polarization relate to surface charge distribution?
When a conductor polarizes, electrons accumulate at one end, creating a negatively charged region, while the opposite end becomes positively charged due to electron depletion. These opposite charges at the surface generate an induced electric field inside the conductor. The surface charge distribution is responsible for creating the internal field that eventually cancels the external field.
Q4: What does Gauss's law tell us about charge inside a conductor?
Gauss's law states that the electric flux through a closed surface equals the enclosed charge divided by permittivity. Since the electric field inside a conductor is zero at equilibrium, the flux is zero, meaning no net charge exists inside the conductor. All excess charge resides on the conductor's surface.
Q5: How long does it take for a conductor to reach electrostatic equilibrium?
A conductor reaches electrostatic equilibrium very quickly when placed in an external electric field. Free electrons rapidly redistribute across the conductor until the induced electric field matches the external field magnitude. This rapid charge redistribution establishes the equilibrium state where the net field vanishes and electron motion ceases.
Q6: What is the relationship between the external field and the induced field inside a conductor?
The induced electric field inside a conductor develops opposite to the external field direction as electrons accumulate at the surface. At electrostatic equilibrium, the induced field magnitude equals the external field magnitude, causing their vector sum to be zero. This balance prevents further charge movement and maintains the zero net field condition.
Q7: Does conductor polarization persist after an external charge is removed?
No, conductor polarization is temporary and depends on the presence of external charges. When the external charge is removed, the separated electrons migrate back and neutralize the positive region. The conductor returns to its neutral state, and the induced electric field disappears.