ELECTROMAGNETIC FIELDS AND WAVES Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016 CONTENTS Maxwell’s Equations Displacement current Plane Electromagnetic Waves – Wave equation Energy Carr[.]
ELECTROMAGNETIC FIELDS AND WAVES Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016 CONTENTS - Maxwell’s Equations - Displacement current - Plane Electromagnetic Waves – Wave equation - Energy Carried by Electromagnetic Waves, Poynting vector Maxwell’s Equations and Electromagnetic Waves • Maxwell discovered that the basic principles of ectromagnetism can be expressed in terms of the four equations that we now call Maxwell’s equations • These four equations are (1) Faraday’s law, (2) Ampere’s law, including displacement current; (3) Gauss’s law for electric fields; (4) Gauss’s law for magnetic fields, showing the absence of magnetic monopoles Review : 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 o E q in E d S closed surface S 0 Review : Gauss’s law of magnetism Gauss’s law of magnetism states that the net magnetic flux through any closed surface is zero: dS B (S) B.dS S The magnetic field lines are closed lines The number of magnetic field lines that exit equal The number of magnetic field lines that enter the closed surface Review: AMPÈRE’S LAW Ampere's law says that the line integral of B.d around any closed path equals μ o I, where I is the total current through any surfaced bounded by the closed path B.d o (C) I r d B + B o I 2r Ii going through _ surface bounded by the closed path it depends on the direction of the current relative to the direction of the line integral that I i or I i B o r H H.d I i (C) i Magnetic filed B is sometimes called magnetic induction, (vector cảm ứng từ) Magnetic field H , magnetic field strength , (cường độ từ trường) Review: Faraday’s law of induction when the magnetic flux through the loop changes with time, there is an emf induced in a loop d B d B.dS dt dt S where B B.dS ( S) is the magnetic flux through the loop Maxwell-Faraday’s equation d E.d dt B.dS (C) S B rotE t Maxwell - Faraday’s equation states that a time varying magnetic field induces an electric field Maxwell -Faraday’s equation states that the emf, which is the line integral of the electric field around any closed path, equals the rate of change of magnetic flux through any surface bounded by that path B(t ) (C) Maxwell- Ampere’s equation Time-changing electric fields induces magnetic fields Displacement current Conduction currents ( motion of charged particles) Time changing electric fields cause Magnetic field also cause Magnetic field => Time changing electric fields is equivalent to a current We call it dispalcement current Displacement current density D E jd o r t t D o r E Electric field E, vector cường độ điện trường Electric Displacement field D : vector cảm ứng điện Maxwell Ampère’s equation D H.d j t .dS (C) S D rotH j t “Line integral of vector H over a closed path (C) is equal to the total current going through any surface bounded by the closed path The total current is equal to the sumof conduction current and displacement current I total I conduction I displcement ( j jd ).dS S ... Displacement current - Plane Electromagnetic Waves – Wave equation - Energy Carried by Electromagnetic Waves, Poynting vector Maxwell’s Equations and Electromagnetic Waves • Maxwell discovered... equation Time-changing electric fields induces magnetic fields Displacement current Conduction currents ( motion of charged particles) Time changing electric fields cause Magnetic field also... (2) Ampere’s law, including displacement current; (3) Gauss’s law for electric fields; (4) Gauss’s law for magnetic fields, showing the absence of magnetic monopoles Review : Gauss’s Law for electric