EXPLAIN WHY AND HOW AMPERE CIRCUITAL LAW FOR STEADY CURRENT WAS MODIFIED TO INCLUDE DISPLACEMENT CURRENT

Introduction

Have you ever wondered how electric circuits work? You may have heard of Ampere's Circuital Law, which describes the relationship between magnetic fields and electric currents in a circuit. However, did you know that this law was modified to include displacement current? In this blog post, we'll explain why and how Ampere's Circuital Law was modified, and provide an example to help you better understand this concept.

 Electric circuits are an essential part of our modern lives. They power our homes, transport systems, and electronic devices. At the heart of electric circuits are magnetic fields and electric currents. One important concept that describes the relationship between these two phenomena is Ampere's Circuital Law. However, the original law did not account for a phenomenon known as displacement current. This blog post will explain why and how Ampere's Circuital Law was modified to include displacement current.

History of Ampere's Circuital Law

 Ampere's Circuital Law was developed by Andre-Marie Ampere, a French physicist who lived in the 19th century. Ampere's law states that the magnetic field generated by a current-carrying conductor is proportional to the current passing through the conductor. The law is expressed mathematically as follows:

∮ B · dl = µ0I

Where B is the magnetic field, dl is a small segment of the loop, µ0 is the permeability of free space, and I is the current passing through the loop.

Ampere's Circuital Law has proved to be an essential tool in understanding the behavior of electric circuits. However, the law only applies to steady currents. Steady currents are those in which the current is constant, and there is no change in the electric field. Ampere's law did not account for the phenomenon of displacement current.

Displacement Current

 Displacement current is a type of electric current that arises in regions of space where there is a changing electric field. Unlike conduction current, which refers to the movement of charged particles through a conductor, displacement current does not involve the actual movement of any charged particles. Instead, it arises due to a changing electric field and can be thought of as a type of "electric field current."

The concept of displacement current was first proposed by James Clerk Maxwell, a Scottish physicist who is widely considered one of the most important figures in the development of modern physics. Maxwell's work on electromagnetism led to the development of Maxwell's equations, which describe the behavior of electric and magnetic fields. Maxwell realized that a changing electric field could give rise to a magnetic field, and vice versa. He also proposed the idea of displacement current to explain how electric fields could behave like currents, even in regions of space where there were no actual moving charges.

Why was Ampere's Circuital Law modified? 

Ampere's Circuital Law, which describes the relationship between the magnetic field and the current passing through a closed loop, was originally formulated for steady currents. However, in the mid-19th century, physicists began to observe phenomena that could not be explained by Ampere's law alone. Specifically, they noticed that the magnetic field in certain regions of space seemed to be changing even though there was no apparent current flowing through the area.

This observation was in conflict with Ampere's Circuital Law, which stated that a magnetic field could only arise due to the presence of a current passing through a closed loop. To explain these observations, physicists realized that a changing electric field could also give rise to a magnetic field, even in the absence of a current. This concept was known as "displacement current."

How was Ampere's Circuital Law modified to include displacement current?

 James Clerk Maxwell, a Scottish physicist, was one of the first to realize that a changing electric field could give rise to a magnetic field. In his original work on electromagnetism, Maxwell formulated a set of equations that described the behavior of electric and magnetic fields. One of these equations was Ampere's Circuital Law.

Modification of Ampere's Circuital Law Maxwell realized that Ampere's Circuital Law needed to be modified to account for displacement current. He did this by adding an additional term to the right-hand side of the equation. This additional term is known as the displacement current density and is denoted by the symbol ɛ0(dE/dt), where ɛ0 is the permittivity of free space and dE/dt is the time rate of change of the electric field. The modified equation, which is known as Maxwell's correction to Ampere's law, can be written as:

∮ B · dl = µ0(I + ɛ0(dE/dt))

This equation is a fundamental component of Maxwell's equations and describes how a changing electric field can give rise to a magnetic field.