Electrostatic Conductor

Introduction

The field of electrostatics dates back to 600 BC. People then already knew about electricity due to the action of friction. But the mathematical formulation of this field of physics happened in the late 18th century with the advent of Coulomb's law of electrostatics. Then the field of electrostatics emerged as a formal field of study.

Later with the discovery of Maxwell's equations, it was found that the electric and magnetic fields are two sides of the same coin. In this tutorial, we will ponder the basic electrostatic properties of the conductors and the reasons behind them in depth.

What is a Conductor?

An ideal conductor is a material medium that has an infinite supply of free electrons. The susceptibility of such materials is ideally infinite meaning that the electric field created inside the ‘meat of the material’ is completely canceled out by the induced charges leaving the material with zero electric fields.

But ideal conductors do not have an infinite amount of free electrons. But they do come very close to the ideal assumption. A single atom in a practical conductor would consist of one free electron.

That would amount to Avogadro’s number of free electrons for almost all the practical cases. And that number is astronomically huge to assume them as perfect conductors.

Field Inside Conductors

Qbrodsky, Field inside conductor, CC BY-SA 4.0

Coulomb Law of Electrostatics

Coulomb’s law of electrostatics states that the electrostatic force between two charged particles is directly proportional to the product of the magnitude of the charges and inversely proportional to the square of the distance between them. The direction of force is away from the point particles for like charges and points towards each other for unlike particles. The mathematical for the law can be stated as,

$$\mathrm{F=K\frac{q_1q_2}{r^{2}}\hat{r}}$$

Where,

K is the proportionality constant $\mathrm{(8.9\: \times\:10^9\:Nm^{2}\:C^{-2})}$

$\mathrm{q_1\:,q_2}$ are the magnitude of the point charged particles

r is the distance of separation of the charged particles

$\mathrm{\hat{r}}$ is the unit vector pointing along the line joining the point particles

This law does not hold for moving charged particles. As the charged particles start moving, the electric field around them starts to distort as a result of space contraction.

This is a relativistic effect. Moreover, there will also be an additional magnetic field to be included in the force expression. Hence, this law is only applicable to statically charged particles.

Electrostatic Properties of a Conductor

• A conductor placed in an electrostatic field will tend to cancel the electric field inside the meat of the material. This is because the electrons in the conductors are completely unbound and free to move around and thus cancel whatever the external field is. If there is some residual field left without cancellation, the electrons will be moving around, which means we’re not dealing with electrostatics anymore. We have to wait till the moving electrons settle down by canceling the field completely. Therefore in electrostatics, the electric field is zero inside the conductor.

• The volume density is zero inside the conductor. This is the basic result from the Gauss law according to which, the electric field is proportional to the volume charge density. Since there are no charges inside a conductor, the volume charge density is zero. This would imply there is no electric field inside the conductor.

• Any charge which is left on the conductor will reside on the surface. This is simply because this is the only configuration that would minimize the potential the most. Hence it is the most favorable configuration.

• The electric field just outside the conductor is perpendicular to the surface. This is because if there is any tangential component of an electric field that will lead to the acceleration of the chargers and it's again not electrostatics anymore. Therefore the charges distributed on the surface of the conductor will arrange themselves such that all the tangential components are killed off.

Electrostatic Shielding

The fact that the electric field is zero inside the conductor can be used to isolate the regions of space from the external electric field. This process of isolating a region of space from any external electrostatic field is called electrostatic shielding. This is because the external electric field applied to a conductor will induce an equal amount of charged particles on the surface which will create their field inside the conductor canceling the external field completely.

The conductor that executes this property is called the faraday's cage. A real-life example would be a car. It is safe to sit inside a car during a thunderstorm as the lighting that would strike the car will pass through the body of it because of electrostatic shielding. Another example would be the design of a coaxial cable. A coaxial cable has a conductor running along its axial center surrounded by an insulator which is further surrounded by another conductor that will shield the inner main conductor electrostatically.

Conclusion

Conductors are a class of materials that most of us are familiar with. Yet understanding their role in applications requires many basic electrostatic ideas. Conductors not only have the above-mentioned applications in the regime of electrostatics. Even the lightning arresters are made of conductors. Their principle of action is simple. Let's say that the cloud carries some charge. When a sharp conductor which is connected to the ground is placed at the top of a building, an opposite charge to that of the cloud will build up on the conductor and it'll start releasing the opposite charges and ionize the cloud and make them neutral. Thus the applications of conductors are not limited. But with a basic understanding of electrostatics, one can easily understand their behavior.

FAQs

Q1. When a conductor is rubbed against a material, will it acquire some charge?

Ans: No. This is because the charges in the conductors are the free electrons. So as long as the rubbing material is in contact with the conductor, the free electrons will neutralize any static charge produced.

Q2. Why do conductors offer resistance if it has free electrons?

Ans: The electrons that carry the current in a conductor suffer random collisions with the atoms in the lattice and with the other electrons. This is under the fact that the resistance of the conductors increases with the increasing temperature. This is due to the increased thermal vibrations of atoms at a higher temperature which makes the maneuvering of electrons tougher.

Q3. Define the ampacity of a conductor.

Ans: The ampacity of a conductor is the amount of current a conductor can conduct without melting down. This depends on the geometry and the nature of the material from which the conductor is built.

Q4. Define isotropic and anisotropic conductors.

Ans: When an external electric field is applied to a conductor, the free electrons will respond by creating a current in the conductor. When this direction of current induced in response to the applied electric field points in the same direction as that of the applied external electric field, then the conductor is said to be an isotropic conductor. And if the direction of current induced in response to the applied electric field points in a different direction to that of the applied external electric field, then the conductor is said to be an anisotropic conductor.

Q5. What is superconductivity?

Ans: Superconductivity is a critical phenomenon where the electrical resistance of the connectors will suddenly drop to zero at extremely low temperatures. This drop to zero resistance will result in the infinite current conductivity of the material. This phenomenon is known as superconductivity and the conductors that exhibit this property are called superconductors.