displacement current derivation by drishti ias
What displacement current is and how it was derived by James Clerk Maxwell?
- Displacement current is a concept in electromagnetism that explains the time-varying electric field in a region of space between two conducting plates that are charged with different potentials. It was introduced by James Clerk Maxwell in his famous set of equations, known as Maxwell's equations.
- Maxwell's equations describe the behavior of electromagnetic waves and how they propagate through space. They are a set of four equations that relate the electric and magnetic fields to their sources, such as charges and currents.
- The equations are as follows:
1. Gauss's law for electricity
2. Gauss's law for magnetism
3. Faraday's law of electromagnetic induction
4. Ampere's law with Maxwell's addition
- Maxwell realized that Ampere's law was incomplete because it did not account for the displacement current, which is the flow of electric field through a region of space that is changing with time. To include this effect, Maxwell added a new term to Ampere's law, which is now known as the Maxwell-Ampere equation. This equation states that the curl of the magnetic field is equal to the sum of the electric current and the displacement current.
- The derivation of displacement current involves the use of Faraday's law of electromagnetic induction and the concept of a changing magnetic field producing an electric field. When a magnetic field changes with time, it induces an electric field in the surrounding space. Maxwell realized that a changing electric field should similarly produce a magnetic field. Thus, he introduced the concept of displacement current to account for this effect.
In conclusion, displacement current is a crucial concept in understanding the behavior of electromagnetic waves and was introduced by James Clerk Maxwell through the derivation of the Maxwell-Ampere equation by displacement current derivation by drishti ias.
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