23.9
Charge on a Conductor
An interesting property of a conductor in static equilibrium is that extra charges on the conductor end up on its outer surface, regardless of where t…
Suppose a lightning bolt strikes a car. The car's body is induced with electric charges on its surface.
Will there be any charges on the car's inner surface?
Here, the car's metallic body can be approximated as a conductor with a cavity.
Since the conductor itself is in electrostatic equilibrium, there should not be any electric field inside the conductor.
Hence, from Gauss' law, the car's inner surface will not have any charge.
Consider another case where a deep, hollow, metal container is connected to an electroscope.
If a positively charged object is lowered into this container, the electroscope deflects, suggesting the presence of electric charges on the container's surface.
This condition can be approximated as a charge enclosed inside a hollow conductor. Due to electrostatic equilibrium and Gauss' Law, the conductor's inner surface acquires negative charges.
As the net charge inside the conductor is zero, the conductor's surface also acquires a net charge opposite to that of the cavity.
Thus, the charges always reside on the surface of a conductor.
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Q1: Why does charge reside only on the surface of a conductor?
In electrostatic equilibrium, the electric field inside a conductor must be zero. By Gauss's law, if there were charge inside the conductor's body, an electric field would exist there. Since this violates equilibrium conditions, all net charge must move to the conductor's surface, where it can arrange to cancel any external fields inside the material.
Q2: What happens to the inner surface of a hollow conductor when a charge is placed inside the cavity?
When a charge is enclosed in a hollow conductor's cavity, the inner surface acquires an induced charge opposite in sign to the enclosed charge. This occurs because electrostatic equilibrium requires zero net charge inside the conductor's material. The induced charge on the inner surface ensures the electric field within the conductor remains zero.
Q3: How does a conductor respond to external charges through its surfaces?
A conductor polarizes in response to external charges, inducing charges on both its inner and outer surfaces. The distribution depends on the conductor's geometry and the location of external charges. At equilibrium, the charge arrangement creates an electric field that exactly cancels external fields throughout the conductor's body.
Q4: Why is there no charge on the inner surface of a conductor with an empty cavity?
For a hollow conductor with no enclosed charge, Gauss's law applied to a surface inside the conductor's material shows zero enclosed charge, so no charge appears on the inner surface. The conductor remains in electrostatic equilibrium with zero electric field inside its material, and any net charge resides only on the outer surface.
Q5: What is the net charge inside a closed conducting container?
The net charge inside a closed conducting container is always zero. If a charge is enclosed and finds a conducting path to the container's surface, it flows outward. If isolated, the enclosed charge induces an equal and opposite charge on the inner surface, maintaining zero net charge within the conductor's material itself.
Q6: How does charge distribute on a conductor with multiple cavities containing different charges?
Each cavity induces opposite charges on its inner surface based on the enclosed charge. The outer surface then acquires a net charge equal to the sum of all enclosed charges. The specific distribution on the outer surface depends on the conductor's geometry, but the total charge always resides on the surfaces, never inside the conductor's material.
Q7: Why does a lightning strike on a car leave no charge on its inner surfaces?
A car's metallic body acts as a conductor in electrostatic equilibrium. When struck by lightning, charge flows to the outer surface. Since the electric field inside the conductor must remain zero, Gauss's law confirms no charge accumulates on inner surfaces or cavities, protecting occupants inside.