Physics 2 - Lecture 3: Electromagnetic Fields and Waves - Huynh Quang Linh

Nội dung text: Physics 2 - Lecture 3: Electromagnetic Fields and Waves - Huynh Quang Linh

1. ELECTROMAGNETIC FIELDS AND WAVES Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016
2. 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
3. Review : Gauss’s law of magnetism Gauss’s law of magnetism states that the net magnetic flux through any closed surface is zero: B.dS 0 dS B S (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.
4. 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 d  B B.dS dt dt S where B B.dS is the magnetic flux through the loop (S)
5. Maxwell- Ampere’s equation 1. Time-changing electric fields induces magnetic fields 2. Displacement current Conduction currents cause Magnetic field ( motion of charged particles) Time changing electric fields also cause Magnetic field => Time changing electric fields is equivalent to a current. We call it dispalcement current. 3. Displacement current density D E jd or Electric field E, vector cường độ điện trường t t Electric Displacement field D : vector cảm ứng điện D orE
6. Maxwell’s equations d B Time changing magnetic fields Maxwell- E.d B.dS rotE dt t induces electric fields Faraday (C) S D D Maxwell – H.d ( j ).dS rotH j Time changing electric fields Ampère (C) S t t induces magnetic fields This law relates an electric Maxwell – D.dS qin dV; divD field to the charge (S) (The distribution that creates it. Gauss for tich V) E-field  the number of magnetic field lines Maxwell – B.dS 0 divB 0 that enter a closed surface must equal Gauss for (S) to the number that leave that surface. B-field There is no magnetic charge. -1 D orE B orH j E : electrical conductivity (.m) ; volume charge density C/m3
7. We have learned equation of the wave on a string y Acos(t kx) y is vertical position of an element of the string dy d2y Asin(t kx); A2 cos(t kx) dt dt 2 dy d2y Aksin(t kx); Ak2 cos(t kx) dx dx 2 2 2  k  v.T v d2y 2 2 dt v2 d2y k 2 dx 2 Wave equation of the Wave on a string 2y 1 2y 0 x2 v2 t2
8. Maxwell’s Maxwell ‘s equation in free Equations space B rotE t I n free space 0, 0, j 0, D B  H,D  E rotH j o o t B divB 0 M - Fadaday's law : rotE t divD E M - Ampère's law : rotB oo j E t D orE M - Gauss's law for B field : divB 0 B orH M - Gauss's law for E field : divE 0
9. E  B  c E B c
10. POYNTING VECTOR  E  B S (W / m2 ) Poynting vector o  E2 S u oc 2 Eo Saverage 2oc u : unit vectoralong thedirection of propagation The magnitude of the Poynting vector represents the rate at which energy passes through a unit surface area perpendicular to the direction of wave propagation The direction of the Poynting vector is along the direction of wave propagation
11. Relationship between Poynting Vector and Electromagnetic Energy Density : Poynting vector is a vector that has the magnitude equal to the energy going through a unit area perpendicular to the wave propagation direction per unit time Energy that goes across area A during time interval dt is contained in the volume with cross section A, length cdt dW wem (A cdt) Energy that goes across a unit area during per a unit time wo A Energy Density dW 1 2 3 cdt S wem.c w  E (J/m ) Adt em 2 o m 2 S wem.c (W / m )
12. Quick Quiz 34.2 What is the phase difference between the sinusoidal oscillations of the electric and magnetic fields in Figure 34.8? (a) 180° (b) 90° (c) 0 (d) impossible to determine ANS: c
13. Example 34.2 An Electromagnetic Wave A sinusoidal electromagnetic wave of frequency 40.0 MHz travels in free space in the x direction as in Figure 34.9. (A) Determine the wavelength and period of the wave. (B) At some point and at some instant, the electric field has its maximum value of 750 N/C and is directed along the y axis. Calculate the magnitude and direction of the magnetic field at this position and time. the magnitude of the magnetic field:
14. Review Statement Write the equation • Maxwell -Faraday’s law states that a changing magnetic field with time (or a changing magnetic flux) induces an electric field. • Maxwell – Ampere ‘s law states that both conduction current and displacement current (the changing electric filed) are the sources of magnetic filed. • Maxwell – Gauss ‘s law for electric fields states that the surface integral of electric field over any closed surface is equal to the total charges enclosed within the closed surface divided by o • Maxwell – Gauss ‘s law for magnetic fields states that the surface integral of magnetic field over any closed surface is 0