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Lecture Physics A2: Electromagnetic Field and Wave - PhD. Pham Tan Thi present the content Maxwell’s equation, Gauss’s law for electric field, Faraday’s law, Ampère’s law with Maxwell’s correction, convert intergral form to differential form, . | Electromagnetic Field and Wave Pham Tan Thi Ph.D. Department of Biomedical Engineering Faculty of Applied Science Ho Chi Minh University of Technology Maxwell s Equation Maxwell discovered that the basic principles of electromagnetism can be expressed in terms of the four equations that now we call Maxwell s equations 1 Gauss s law for electric fields 2 Gauss s law for magnetic fields showing no existence of magnetic monopole. 3 Faraday s law 4 Ampere s law including displacement current Maxwell s Equations Integral form Differential form Gauss I Law Qinside E dS r E quot 0 quot 0 Gauss Law for Magnetism I dS B 0 0 r B Faraday s Law I d B @ B E dl r E dt @t IAmpere s Law d E @ E B dl µ0 Ienclosed µ0 quot 0 µ0 J µ0 quot 0 r B dt @t Macroscopic Scale Microscopic Scale Gauss s Law for Electric Field The flux of the electric field the area integral of the electric field over any closed surface S is equal to the net charge inside the surface S divided by the permittivity ε0. I Qinside E dS quot 0 Qinside E dxdyˆ n n dS ˆ dS n ˆ dxdy quot 0 Qinside E dxdycos quot 0 dx Qinside dS Edxdy dy quot 0 2 Qinside ES E 4 r quot 0 Qinside E Coulomb s Law 4 r2 quot 0 Gauss s Law of Magnetism Gauss s law of magnetism states that the net magnetic flux through any closed surface is zero I dS B 0 The number of magnetic field lines that exit equal to the number for magnetic field lines that enter the closed surface E I Qinside dS E quot 0 Faraday s Law The electric field around a closed loop is equal to the negative of the rate of change of the magnetic flux through the area by the loop. I d l d B d l Edlcos Ed E E dt Edl θ 0 d B E 2 R dt d B e.m.f dt d B W F d Eqd e.m.f dt W Ed d V Ed e.m.f Ampère s Law with Maxwell s Correction The line integral of magnetic field over a closed path is equal to the total current going through any surface bounded by the closed path I d E B dl µ0 Ienclosed µ0 quot 0 dt 1. Time-changing electric fields induces magnetic fields 2. Displacement current .
