Tiêu đề SP-4_Ch-23_Electromagnetic Waves.pdf ✅

Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 Chapter Contents Introduction Ampere circuital law and its application Displacement Current Maxwell’s Equations Sources of Electromagnetic Waves Important characteristic and Nature of Electromagnetic Waves Relation Between Electric Field, Magnetic Field and Speed of Light The Poynting Vector Intensity of Electromagnetic Wave Intensity due to a Point Source/Line Source/Plane Source Hertz’s Experiment Electromagnetic Spectrum Introduction Electromagnetic waves in the form of visible light enable us to view the world around us. Infrared waves warm our environment. Radio waves carry our favourite TV and radio programs and the list goes on and on. In this chapter, we will study regarding displacement current, electromagnetic waves and its various parts and their uses. AMPERE CIRCUITAL LAW AND ITS APPLICATION Let us consider a parallel plate capacitor which is being charged as shown in the figure. If at an instant charge on the capacitor is Q, and the instantaneous value of current in the connecting wire is I, then dQ I dt  + + + + + + I I I x y EMF Source A1 A2 I – + Consider two surface A1 and A2 are bounded by a closed loop xy. The surface A1 lies between the two plates of capacitor and A2 outside the plates. The area A2 is pierced by the current I but area A1 is not pierced by this current. Therefore for surface A2 0 B dl I .    For surface A1 B dl . 0   Thus there is an apparent contradiction in applying ampere circuital law in this situation. Chapter 23 Electromagnetic Waves
166 Electromagnetic Waves NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 DISPLACEMENT CURRENT “Displacement current is a current which is produced due to the rate of change of electric flux with respect to time”. Displacement current is given by I d = 0   E d dt   + + + + + + P I I x y EMF Source A1 A2 This current I d is the missing term in Ampere’s law passes through the surface – + A1 and is known as Maxwell displacement current. Note : (i) For consistency of Ampere circuital law, there must be a current between the plates of capacitor. It is called displacement current (Id) because it is produced by changing electric field or electric displacement. (ii) The current in conductor is due to the flow of charge carrier hence called conduction current Ic. (iii) In modified Ampere circuital law, “the line integral of magnetic field along a closed loop in free space is equal to 0 times the total current (sum of conduction and displacement) threading the loop.” 0 . ()  B dl I I   c d Example 1 : Show that displacement current is equal to conduction current during charging of a capacitor. Solution : Let at an instant magnitude of charge on the plates of capacitor be Q. Area of each plate is A. Electric field between the plates of capacitor 0 Q E A   ...(i) Flux of this field passing through the surface between the plates is E = E × A = 0   Q A A + + + + + + I I EMF Source A A Q – Q 0 E Q    ...(ii) Displacement current I d is 0 E d d I dt    = 0 0 d Q dt         = 0 0 1 dQ dt    d dQ I dt  ...(iii) dQ dt is the rate at which charge is reaching to positive plate of capacitor through conducting wire therefore c dQ I dt  ...(iv) From equations (iii) and (iv) I d = I c Example 2 : A parallel plate capacitor consists of two circular plates of radius R = 0.1 m. They are separated by a distance d = 0.5 mm. If electric field between the capacitor plates changes as 13 –1 –1 5 10 V m s . dE dt   Find displacement current between the plates. Solution : Area of plates A = r 2 = 3.14 × (0.1)2 m2
NEET Electromagnetic Waves 167 Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 13 –1 –1 5 10 V m s dE dt   0 E d dE dE d IA A dt dt dt                 ∵ = 2 12 2 2 13 2 C V 8.85 10 3.14 (0.1) m 5 10 N m m s      I d = 13.9 A MAXWELL’S EQUATIONS Maxwell’s equations relate electric field E and magnetic field B and their sources which are electric charges and current. In free space Maxwell’s equations are as follows. (i) enclosed 0 . .    q E ds This equation represents Gauss’s law in electrostatics, which states that net electric flux through any closed surface equals to 0 1  times the total charge enclosed by the surface. (ii) B ds . 0.   This equation is considered as Gauss’s law in magnetism. It states that net magnetic flux passing through a closed surface is zero. It implies that number of magnetic field lines entering the closed surface is equal to number of magnetic line leaving the closed surface, that is magnetic field does not start or end at a point therefore there is no isolated magnetic monopoles. (iii) . .     d B E dl dt This equation is Faraday’s law of electromagnetic induction. This law relates electric field with changing magnetic flux. “Induced current in a conducting loop placed in a region in which magnetic field is changing with respect to time confirms this equation.” (iv) 0 0 . E C d B dl I dt           . This equation represents Ampere-Maxwell’s law or generalised form of Ampere’s law. This law states that “ line integral of magnetic field along a closed loop is equal to 0 times the total current threading the area bounded by the closed loop”. This law describes how a magnetic field can be produced by both changing electric flux and a conduction current. SOURCES OF ELECTROMAGNETIC WAVES “The waves that are produced by accelerated charged particles and composed of electric and magnetic field vibrating transversely and sinusoidally perpendicular to each other and to the direction of propagation are called electromagnetic waves or electromagnetic radiations.” These waves are produced in the following physical phenomena : (i) An electric charge at rest produces only electrostatic field around it. (ii) A charge moving with uniform velocity (i.e. steady current) produces both electric and magnetic field, here magnetic field does not change with time hence it does not produce time varying electric field. (iii) An accelerating charge produces both electric field and magnetic field which varies with space and time which forms electromagnetic wave. (iv) An accelerating charge (in case of LC oscillation) emits electromagnetic wave of same frequency as frequency of accelerating charge (i.e., frequency of oscillating LC circuit)
168 Electromagnetic Waves NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 (v) An electron orbiting around nucleus in a stationary orbit does not emit electromagnetic wave. It will emit only during transition from higher energy orbit to lower energy orbit. (vi) Electromagnetic wave (X-ray) is produced when high speed electron strikes a target of high atomic number and high melting point. (vii) Electromagnetic wave (-rays) is produced during de-excitation of nucleus in radioactivity. IMPORTANT CHARACTERISTICS AND NATURE OF ELECTROMAGNETIC WAVES (i) It is produced by accelerated charge (e.g., X-ray) and oscillating charge (e.g., LC oscillation). (ii) It travels in free space with speed equal to 3 × 108 m/s which is given by 0 0 1 . μ c   (iii) These waves do not require material medium for their propagation. (iv) In these waves E B and -vary sinusoidally. E B and y B x z become maximum at same place and at the same E time, but perpendicular to each other as well as to direction of propagation. Therefore the phase difference between the two fields is zero. The amplitude of electric and magnetic fields are related to each other as 0 0 E c B  . The direction of propagation can be determined by E B . (v) The velocity of electromagnetic wave in a medium is decided by electric and magnetic properties of medium not by the amplitude of electric and magnetic field vector. The speed of electromagnetic wave in a medium is 1 v  .   (vi) The energy carried by electromagnetic wave is equally divided between electric field and magnetic field. Total average energy density 2 2 0 0 0 0 1 1 2 2 B U E    . (vii) Electric field vector of an electromagnetic wave produces optical effect hence it is also known as light vector. (viii) Electromagnetic wave is not deflected by electric field as well as magnetic field because it consists of uncharged particles called photon. (ix) Intensity of electromagnetic wave is defined as “energy crossing per second per unit area perpendicular to direction of propagation of electromagnetic wave.” Average intensity is given by 2 2 0 0 0 r.m.s. 1 or 2 I Ec E c   (in terms of electric field) 2 2 0 rms 0 0 1 2 B B Ic c     (in terms of magnetic field) (x) Electromagnetic waves carry energy as well as momentum. Momentum U p c  U = Energy carried by electromagnetic wave in free space. c = Speed of EMW in free space.