23.9:
Charge on a Conductor
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.
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 they originate. Consider a hollow metallic conductor with a uniform surface charge density. Since the conductor itself is in electrostatic equilibrium, there should not be any electric field inside the conductor. Now, assume a Gaussian surface enclosing the hollow portion. Applying Gauss's law, the inner surface of the hollow conductor will not have any charge.
Now, suppose a charge is enclosed inside the hollow conductor. Due to electrostatic equilibrium and Gauss's law, the conductor's inner surface acquires a negative charge. As the net charge inside the conductor is zero, the conductor's surface also acquires a net charge opposite to the cavity. Thus, the charges always reside on the surface of a conductor.
Consider another conductor with two cavities, 1 and 2. Cavity 1 encloses a positive charge, while cavity 2 encloses a negative charge. The polarization of the conductor results in induced negative and positive surface charges, respectively, on the inside surface of cavities 1 and 2, respectively. Similarly, the outside surface of the conductor shows an induced charge equal to the difference between the positive and negative induced charges inside the cavities.
The distribution of charges on the surfaces depends upon the geometry. At electrostatic equilibrium, the charge distribution in a conductor is such that the electric field by the charge distribution in the conductor cancels the electric field of the external charges at all points inside the conductor's body.
In summary, the net charge inside a closed conducting container is always zero. If the closed conducting container encloses a charge and the charge finds a conducting path, it flows to the container's surface. Else, the enclosed charge induces an equal and opposite charge on the inner surface, so the net charge inside is still zero. Any net charge on a conducting object resides on its surface.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from 6.4 Conductors in Electrostatic Equilibrium – University Physics Volume 2 | OpenStax
- Young, H.D and Freedman, R.A. (2012). University Physics with Modern Physics. San Francisco, CA: Pearson. Pp. 741-743