Maxwell-Ampere Law
The progress in the theory of displacement current can be traced back to a famous physicist named James Clerk Maxwell. Maxwell is well known for Maxwell’s Equations. The combination of four equations demonstrates the fundamentals of electricity and magnetism. For displacement current, we will be focusing on one of these equations known as the Maxwell-Ampere law.
Before Maxwell, Andre-Marie Ampere had developed the famous equation known as Ampere’s law. This law relates the magnetic field (B) surrounding a closed loop to the conduction current (I) traveling through that loop multiplied by a constant known as the permeability of free space (μ0).
∫B . ds = μ0I
Whenever there is continuous conduction current Ampere’s law holds true, but there are cases when problems arise in the law as it’s written. For example, a circuit with a capacitor in it. When the capacitor is charging and discharging, current flows through the wires creating a magnetic field, but between the plates of the capacitor, there is no presence of current flow. According to Ampere’s law, there can be no magnetic field created by the current here, but we know that a magnetic field does exist. Maxwell realized this discrepancy in Ampere’s law and modified it in order to resolve the issue.
∫B . ds = μ0 (I + ε0 (dφE /dt))
This final form of the equation is known as the Maxwell-Ampere law.
The part Maxwell added to it is known as displacement current (Id), and the formula is,
Id = ε0 (dφE /dt)
The above equation consists of two terms multiplied together. The first is known as the permittivity of free space (ε0), and the second is the derivative with respect to time and electric flux (φE). Electric flux is the rate of flow of an electric field through a given area. By taking its derivative with respect to time, we consider the change in that rate of flow over time.
Displacement Current
Displacement current is the current that is produced by the rate of change of the electric displacement field. It differs from the normal current that is produced by the motion of the electric charge. Displacement current is the quantity explained in Maxwell’s Equation. It is measured in Ampere. Displacement currents are produced by a time-varying electric field rather than moving charges.
In this article we will learn about, displacement current, its characteristics, and others in detail.