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Electrostatics Class 12: 4 Important Concepts for JEE-Main

If I had to choose one topic in physics to set the entire JEE Main paper upon, Electrostatics would be it. The vastness of concepts, tricks, ideologies, logic, and what-not available on this topic makes it my personal favorite for testing the real thinking and problem solving capacity of any JEE aspirant.

electrostatics, jee main -magooshImage By Husna Ghaffar

What Is an Electric Charge?

Electrostatics — as the name suggests — is the study of electric charges at rest (in the realm of classical physics). But what is an electric charge? It may be hard to define charge but just to give you an idea: suppose you run a spoon through oil, and then graze it over a very small (caution here) piece of paper. You’ll notice the piece of paper getting attracted to it. This attraction is due to a phenomena of charge induction, or simply put, due to the presence of a charge on the body

Now that you understand the context, let me put up some bizarre rules. “Like charges repel each other and unlike charges attract each other.”

This statement refers to the way charges are defined. A positive charge attracts a negative or uncharged object, but repels a positively charged object, and vice versa.

It’s interesting to note that if charges attract or repel each other, there must be a governing law for the same. The answer to this problem was posted by Newton when he gave an analogy between gravitation and electrostatics (more on that later). He concluded experimentally, that two charges (points Q1 and Q2), at rest placed at a distance (R) from each other exert a force on one another. This force is proportional to the product of the magnitude of the individual charges and inversely proportional to the square of the distance between them. The constant of proportionality K has a value equal to 9*109 in SI units and 1 in CGS units. This K is dependent on the surroundings of the two charges.

What Is an Electric Field?

Electric Field is another important parameter in the study of Electrostatics. This term gets its definition from the Force relation only. It is the force exerted by a charge on a test charge (+ve and very small magnitude) which is placed at a distance (R) from it. Electric Field calculations are quite vital in both JEE Main and Advanced. Though most problems are solvable by integration, there are some tricks and short cuts to bypass integration or at least simplify it.

Electric Flux and Gauss Law

One such application involves the concept of Electric Flux and the famous Gauss Law. Electric flux is defined for an electric field as the measure of number of field lines crossing a unit area per unit time. This can be considered somewhat similar to density of field lines in an electrostatic field. The Gauss Law, relates electric flux due to a charge distribution over a surface to the quantity of charge present strictly inside the surface.

The Law states that Flux passing through a closed surface is equal to the quantity of charge inside divided by permittivity of vacuum which is equal to 8.85*10-12 in SI units. The point to be noted here is that flux can also be defined as surface integral of Electric Field due to some charge distribution over a closed surface. The Gauss Law stated above simplifies the calculation of electric field to a great extent in case of symmetry elements. For example, calculations for electric field inside a solid sphere with uniform volume charge density can be easily calculated using this law. You don’t need to integrate, just use concepts of symmetry and calculate charge inside the surface by using the uniform nature of charge distribution.

Various Types of Energies

Another very important concept in Electrostatics for the JEE is Interaction Energy between a system of discrete or continuous charges. However, calculating this requires the use of electric fields too, highlighting why electric fields have been a hot topic on the exam. Interaction energy can be loosely defined as the energy required to arrange the system in given conditions from infinite separation reversibly. The word reversible here refers to assembling the system in a very slow manner, ie: no acceleration for any of the charge by applying a variable force at each instant which just balances the electrostatic force.(Not doing so, changes the chapter).

electrostatics, energy systems - magooshImage By Dmitriy Rybin
 
Self Energy of a system is new favorite for JEE paper setters. Self energy of a point charge is ideally not defined but if you want to give it mathematical form, it would be very high. For other charge distributions, this refers to energy of making the system.

It is necessary to understand the difference between the two energy terms.

  • Interaction energy refers to energy of attraction or repulsion between two or more systems,
  • whereas Self Energy refers to energy required to make the system.

Self energy is always positive since you have to do work to assemble the system, no charge wants by itself to leave infinite separation and come in an ordered state (Entropy Considerations, can somehow be related here).

Total energy of a pair of systems is the summation of Self Energy and Interaction Energy of the two. It is this total electrostatic energy which is conserved, the individual energies might change. So I would suggest while solving the JEE paper, be careful what to conserve and what to change.

Some good books to refer to for this very important topic would be – H.C.Verma, Electricity and Magnetism by DC Pandey.

I hope all this information helped introduce you to the various portions of electrostatics that you will surely be tested on!

Wishing you best of luck, Cheers!

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