5. Lecture 05 Av 335 - Displacement Current_Maxwell's Eqs in final form.pptx

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1. Lecture No 5 Displacement Current and Maxwell’s Equations in Final Form Book(s) consulted: Elements of Electromagnetics, Matthew, N. O. Sakidu Chapter 9, Section 9.4, 9.5 AV-335 Transmission lines and waveguides Dr. Hidayat Ullah 23/05/202 4 AV-335 TL & WG 1 /12

2. Previous Lecture Electromotive Forces: AV-335 TL & WG Transformer EMF: a stationary loop in a time-varying B field Motional EMF: a time-varying loop area in a static B field Hybrid - Moving Loop in time-varying Field: a time-varying loop area in a time-varying B field 2 /12

3. Concept of Displacement Current AV-335 TL & WG James C. Maxwell proposed the concept of displacement current to correct the violation of Ampere’s law by taking account for the production of magnetic fields in empty space 3 /12

4. Displacement Current Previously we have essentially reconsidered Maxwell’s curl equation for electrostatic fields and modified it for time-varying situations to satisfy Faraday’s law. We shall now reconsider Maxwell’s curl equation for magnetic fields (Ampère’s circuit law) for time varying conditions. For static EM fields, we recall that But the divergence of the curl of any vector field is identically zero The continuity of current in eq. (5.43), however, requires that AV-335 TL & WG 4 /12

5. Displacement Current We must modify eq. (9.17) to agree with eq. (9.19). To do this, we add a term to eq. (9.17) so that it becomes AV-335 TL & WG Incompatible (9.17) (9.19) 5 /12

6. Generalized Ampere’s Law – Maxwell’s Equation This is Maxwell’s equation (based on Ampère’s circuit law) for a time-varying field. The insertion of J d into Ampere’s Law was one of the major contributions of Maxwell. Without the term Jd , the propagation of electromagnetic waves (e.g., radio or TV waves) would not be impossible. At low frequencies, Jd is usually neglected compared with J. However, at radio frequencies, the two terms are comparable. The concept was not experimentally verified at that time. It was years later that Hertz succeeded in generating and detecting radio waves, thereby verifying it. AV-335 TL & WG 6 /12

7. Displacement Current Based on the displacement current density, we define the displacement current as We must bear in mind that displacement current is a result of time-varying electric field. A typical example of such current is the current through a capacitor when an alternating voltage source is applied to its plates AV-335 TL & WG 7 /12

8. Example 9.4 AV-335 TL & WG 8 /12

9. Please Read… AV-335 TL & WG The Scottish physicist James Clerk Maxwell (1831–1879) is regarded as the founder of electromagnetic theory in its present form. Maxwell’s celebrated work led to the discovery of electromagnetic waves. Through his theoretical efforts when he was between 35 and 40 years old, Maxwell published the first unified theory of electricity and magnetism. The theory comprised all previously known results, both experimental and theoretical, on electricity and magnetism. It further introduced displacement current and predicted the existence of electromagnetic waves. Maxwell’s equations were not fully accepted by many scientists until 1888, when they were confirmed by Heinrich Rudolf Hertz (1857–1894). The German physicist was successful in generating and detecting radio waves. 9 /12

10. Maxwell’s Equations AV-335 TL & WG When we allow the fields to vary with time, then it is possible to use them for signal transmission Maxwell’s equations is a set of equations that govern the fields at every point in space and at all times and it is also an extension of physical laws to time varying situations For a field to “qualify” as an electromagnetic field, it must satisfy all four Maxwell’s equations. 10 /12

11. 9.5 MAXWELL’S EQUATIONS IN FINAL FORMS AV-335 TL & WG 11 /12

12. Reading Assignment Section 9.5: Associated equations associated with Maxwell’s equations, such as, Lorentz force equation, Continuity equation, boundary conditions for time-varying situations, etc. Time Harmonic Fields AV-335 TL & WG 12 /12 NEXT TIME