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@aboveengineering Maxwell's Fourth Equation Derivation | Modified Ampere's Law & Displacement Current | Engineering Physics In this lecture of **Engineering Physics**, we derive and explain **Maxwell's Fourth Equation**, which is the **Modified Ampere’s Circuital Law**. This equation is unique because Maxwell added a crucial term called *Displacement Current ()* to the original Ampere's Law. This correction resolved the inconsistency in the law for time-varying fields (like in a capacitor) and unified electricity and magnetism, proving that light is an electromagnetic wave. We will start by showing why Ampere's original law fails for capacitors, define Displacement Current, and then derive the final differential form . --- 🔗 Previous Lecture Links: 🔗 Important Playlists & Links: Lecture – Maxwell's 4th Equation (Ampere's Law):* [ • Equation of Continuity Derivation | Conser... ] *Lecture – Maxwell's 3rd Equation (Faraday's Law):* [ • Maxwell's Third Equation Derivation | Fara... ] **Lecture – Maxwell's 1st Equation (Gauss Law):**[ • Maxwell First Equation : Derivation in eas... ] *Lecture – Maxwell's 2nd Equation (Magnetism):* [ • Maxwell 2nd Equation Derivation || Easy st... ] • Trapezoidal Method to find Area || Basic c... • BETA and GAMMA functions explained || Engi... • Relation between Beta & Gamma function || ... • Otto Cycle Explained | PV & TS Diagram | E... • What is Divergence || engineering physics ... • Gauss Divergence Theorem with Proof || Der... • Maxwell Equations Explained || Full concep... 📌 Topics Covered in This Lecture: *Statement of Maxwell's 4th Equation* – The need for modification. *Inconsistency of Ampere’s Law* – Why failed. *Concept of Displacement Current* – Continuity of current through a capacitor. *Derivation of Differential Form* – Adding the term. *Integral Form* – . *Physical Significance* – How changing Electric fields produce Magnetic fields. --- 🔔 Stay Connected: 👉 *Join Our Telegram Group (Notes, PYQs & Updates):* [https://t.me/1PJ1V29Wm0NiNDll](https://t.me/1PJ1V29Wm0NiNDll) Maxwell fourth equation derivation modified ampere circuital law displacement current explained maxwell equation differential form inconsistency of ampere law conduction current vs displacement current rgpv engineering physics unit 1 electromagnetic theory btech 1st year curl of magnetic field derivation of maxwell's 4th equation maxwell equations one shot time varying electric field continuity equation physics for engineers maxwell equations in hindi integral and differential form importance of displacement current electromagnetic waves propagation magnetic field generation above engineering channel physics exam preparation engineering physics notes pdf vtu physics module 2. #maxwellequations #ampereslaw #displacementcurrent #engineeringphysics #electromagnetism #rgpv #btechphysics #aboveengineering #physicsderivation #calculus #science #engineeringstudent #physicsclass #examready maxwell fourth equation derivation, modified ampere circuital law, displacement current explained, maxwell's 4th equation, ampere's law modification, engineering physics electromagnetism, integral to differential form, time varying electric field, rgpv physics, btech 1st year physics, curl of magnetic field, physics for engineers, above engineering, derivation of maxwell equations, maxwell equations in hindi, conduction vs displacement current, electromagnetic theory, magnetic field intensity ⚖️ COPYRIGHT DISCLAIMER Copyright Disclaimer Under Section 107 of the Copyright Act 1976, allowance is made for "Fair Use" for purposes such as teaching, scholarship, comment, and research. Non-profit, educational, or personal use tips the balance in favor of fair use. 📢 *Subscribe to @aboveengineering* to 'Rise Above Average' and master your Engineering subjects!