Electrostatics of Conductors: Properties, Applications and Solved Examples

The study of electric charges at rest inside an electrical conductor is known as electrostatics of conductors. Electrostatics of conductors works only in a stationary medium; if any other discrete charge interacts with the system, then the intensity of that electric field becomes undefined.

In this article, you will learn about the basics of electrostatics of conductors, their properties, applications and solved examples.

Electrostatics of Conductors

In an electric conductor, in static and dynamic conditions, i.e, under the influence of an external electric field or not, the final electric field at every point of that electric charge is zero.

In conductors the free electrons are nothing but the valence electrons of a particular atom, but, in electrolytes, both the positive and negative ions are mobile. These free electrons experience a drift when they experience an electric field. They disperse inside the conductor in such a way that the final electric charge at every point is zero.

Electrostatic Properties of Conductors

The following are the properties of electrostatic conductors:

1. The net charge of the electric field inside a conductor is zero according to the Gauss’ theorem. We know that a conductor has free electrons, and that these electrons wander or are forced by an electric field. These electrons inside the conductor are distributed such that the net electric field at any given point within the conductor is zero.
   The integral form of the Gauss theorem is given by
   
2. The total electric charge is always conserved.
3. The interaction between any two charges is completely unaffected by the presence of other charges and is inversely proportional to the square of the distance separating them.
4. The electrostatic force is always normal (or perpendicular) to the charged surface at every point and satisfies the superposition principle. A component of the electric field in the static condition would have been present along the surface of a conductor if the electric field lines were not normal at the surface. Thus, free charges on the surface would have encountered some force, which causes their motion but this really occurs. The forces must be normal to the surface since there are no tangential components.
5. There is no internal charge in a conductor under static conditions.
6. In a conductor, the electrostatic potential throughout the volume of the conductor is constant at any point. It’s value at the surface is the same at any point within the conductor.
7. Every point charge, whether it is inside an electric conductor or not, will always produce its own electromagnetic wave.
8. The flux of an electric field through any closed surface, of a conductor, is 1/𝛆₀ times the electric charge.

Application of Electrostatics of Conductors

There are many practical applications to the electrostatics of conductors

1. Van de graff generator 
2. Photocopiers
3. Smoke precipitators
4. Industrial air cleaning filters
5. Laser printers and inkjet printers
6. Faraday cage

Apart from that, they are also used in a static medium to find the electric flux for a closed charged Gaussian surface, the intensity of the electric field lines (Coulomb’s Law) and so on.

Solved Examples on Electrostatics of Conductors

Example 1. Find the field outside a uniformly charged solid sphere of radius R and total charge q.

Solution. Consider a charged solid sphere with radius R,

Here R > r ,

The above figure is called the Gaussian surface in the trade.

According to the Gauss’ Law , for any enclosed surface ,

 

The magnitude E is constant over the Gaussian surface,

Then ,

=

this is the electric field outside a uniformly charged sphere

Example 2. What would be the force (F) acting on an electric field on two charges, q1 = 1.2C and q2 = 2.4C, at a distance of 2 m?

Solution. Given data:

q1= 1.2C

q2= 2.4C

R= 2 meters

 

By Coulomb’s Law ,

F =

Example 3. Statement 1: Gauss’ Law is based on the inverse square dependence on distance. Statement 2: If a Gaussian surface passes through another discrete charge then the electric field does remain well defined.

1. Both statements 1 and 2 are right.
2. Both statements 1 and 2 are wrong.
3. Statement 1 is right and statement 2 is wrong.
4. Statement 2 is right and statement 1 is wrong.

Solution. Option (c ) is correct because if a Gaussian surface passed through another discrete charge then the electric field is undefined.

Hope this article was informative and helpful for your studies and exam preparations. Stay tuned to the Testbook app for more updates and topics related to Physics and various such subjects. Also, reach out to the test series available to examine your knowledge regarding related exams.