Chapter 8 Electromagnetic Waves PDF

a. ELECTROMAGNETIC WAVES WAX James Clerk Maxwell proposed that just like a magnetic field changing with time produces an electric field, a time varying electric field also produces a magnetic field....

a. ELECTROMAGNETIC WAVES WAX James Clerk Maxwell proposed that just like a magnetic field changing with time produces an electric field, a time varying electric field also produces a magnetic field. Maxwell formulated a set of equations involving electric and magnetic field. The Maxwell equations along with Lorentz force formula mathematically express all the basic laws of Electromagnetism Unification of Electricity, Magnetism and Light Maxwell’s equation predicted the existence of electromagnetic waves. The speed of the wave according to these equations came out to be very close to the speed of light (c= 3 × 108 m/s) obtained by measurements. This led to the conclusion that light is an electromagnetic wave. Mx Displacement current (PYQ 2018, 2016) The current produced due to changing electric field (electric displacement) is called displacement current. Consider a capacitor C. Let us observe the process of charging the capacitor and apply Ampere’s Circuital Law – To find the field at a point P just outside the capacitor, consider a plane circular loop of radius r with its plane perpendicular to the direction of the current carrying wire. From symmetry we can say that the field is directed along the circumference of the loop and is of the same magnitude at all points. Therefore- Now consider another surface with the same boundary and a pot like surface and has its bottom between the plates of the capacitor (fig i) and another surface like a tiffin box (fig ii) (all three are of the same perimeter). Applying ACL to them, we find that the left side of the equation has not changed but the right side becomes 0 as no current passes through the surface. Therefore, we conclude a term must be missing from ACL. to find this missing term, consider the electric field passing between the two plates. Let the charge on the plates be Q, Area A then the magnitude of field between the BoB fields- H µ, The flux through surface- Now if there is any current through the surface of the capacitors , it can be written as i= dQ/dt This is the missing term in Ampere’s circuital law and is called the displacement current (id)  Note: 1. The total current carried by conductors due to flow of charges is called the conduction current (ic) 2. Thus Maxwell concluded that the source of magnetic field is not just the conduction current but also the rate of change of electric field w.r.t. time. I.e. the total current is the sum of conduction current and displacement current- Outside the capacitor there is only conduction current and inside the capacitor, there is only displacement current. Wx Ampere-Maxwell Law (Modified Ampere’s circuital law) (PYQ 2020, 2016) The total current passing through any surface of which the closed loop is the perimeter is the sum of the conduction current and the displacement current. Note: There are regions where there is no conduction current but only displacement current for e.g. between the plates of a charging/discharging capacitor And there are regions where there is only conduction current and no displacement current for e.g. a wire carrying steady current or outside a capacitor. (PYQ 2018) Wx Maxwell’s Equations The following five equations are called Maxwell’s equations- four 1) 2) 3) 4) Important PYQs ties Ques: Write the mathematical form of Ampere- Maxwell law (PYQ 2020) [1M] Ans: Ques: Give one example each to illustrate where there is i) displacement current but no conduction current ii) only conduction current but no displacement current (PYQ 2018) [1M] Ans: i) Between the plates of a charging/discharging capacitor ii) outside the capacitor plates Ques: Write Maxwell’s generalization of ACL. Show that in charging a capacitor, the current produced within the plates of a capacitor is -  Where ɸE is the electric flux produced during charging of the capacitor plates. (PYQ 2016) [3M] Ans: Exactly as given in notes. o NCERT example 8.1 A parallel plate capacitor with circular plates of radius 1m has a capacitance of 1nF. At t=0, it is connected for charging in series with a Resistor R= 1MΩ across a 2V battery. Calculate the magnetic field at a point P, halfway between the center and the periphery of plates after t= 10-3s (the charge on the capacitor at time t is q=CV [1- e-t/τ] where time constant τ= CR) ( since r=1m) Consider a loop of radius 0.5 m parallel to the plates passing through P. The magne@c field B is along the loop and has the same value at all points. Electric flux through the loop- The displacement current - Using Ampere-Maxwell law we get- Wx Source of Electromagnetic waves (PYQ 2016) Accelerated charges produce electromagnetic waves. Consider a charge oscillating with some frequency (oscillation is an example of accelerated motion). This produces an oscillating electric field in space which is the source of an oscillating magnetic field which is in turn source for an oscillating electric field and so on. So, the oscillating electric and magnetic fields regenerate each other, so as to speak, the wave propagates through space. The frequency of the wave is the frequency of the oscillating charge and the energy of the wave comes from the energy of the source charge. Wx Nature of Electromagnetic waves (PYQ 2016, 2013) - Electric and magnetic fields in an EM wave are perpendicular to each other and to the direction of propagation. - The electric and magnetic fields oscillate in phase with each other and the direction of energy transfer (velocity of wave) is given by E × B. Consider an em wave travelling in the z direction. The electric field Ex is along the x axis and magnetic field By is along the y axis. The electric and magnetic fields are perpendicular to each other and to the direction of propagation. We can write Ex and By as- Ex = E˳ Sin(kz-ωt) By = B˳ Sin(kz-ωt) Where k is the wave number and is given by-  And ω is the angular frequency of the wave. The speed of propagation of the wave is given by- Also, from maxwell’s equations, we can conclude that- Note: rms Velocity of EM wave in any medium- i.e. the speed of em wave does not depend on the electric and magnetic field but on the electric and magnetic properties of the medium. Xx Energy and Energy density of EM waves (PYQ 2019) From Maxwell’s equations, it can be derived that- Where µE and µB are the instantaneous electric and magnetic energy density respectively Note: The instantaneous electrical and magnetic energy densities are equal. Proof: Therefore, the net instantaneous energy density- The average net energy density- :3 Important PYQs the ¥ Ques:. Prove that the average energy density of the oscillating electric field is equal to that of the oscillating magnetic field (PYQ 2019) [2M] Ans: Mx Properties of EM waves (PYQ 2017, 2012) 1. Electromagnetic waves do not require a material medium to propagate- no material medium is involved in vibration of electric and magnetic fields. Note: Scientists in the 19th century thought that there must some material medium present in all space and matter for EM waves to propagate. They called this medium Ether. This theory was disproved by the experiment of Michelson and Morley. 2. Electromagnetic waves can be polarized 3. The speed of Electromagnetic waves in free space or vacuum is a fundamental constant. C= 3 × 108 m/s 4. Electromagnetic waves carry energy and momentum- Since EM waves contain both Electric and Magnetic fields therefore, there is a non-zero energy density associated with them. Consider a plane perpendicular to the direction of propagation. All the charges in this plane will be set in sustained motion due to the electric and magnetic field. the charges thus acquire momentum and energy from the wave. If the total energy transferred to a surface is U in time t, it can be shown that the magnitude of total momentum (p) delivered to this surface (for complete absorption) is- 5. Electromagnetic waves exert pressure- Since the waves carry momentum, they also exert pressure. This is called radiation pressure. Note: Intensity of wave- Important PYQs ¥E÷F? Ques: Do electromagnetic waves carry energy and momentum? (PYQ 2017) [1M] Ans: Yes, electromagnetic waves carry energy and momentum. Ques: How are EM waves produced by oscillating charges. Draw a sketch of linearly polarized em waves propagating in the Z-direction. Indicate the direction of oscillating electric and magnetic field (PYQ 2016, 2013) [3M] Ans: exactly as given in notes Ques: How are the magnitudes of the electric and magnetic fields related to the velocity of the EM wave? (PYQ 2013) [1M] Ans: - Ques: Name the property which remains constant for microwaves of wavelength 1mm and UV radiations of 1600 A° in vacuum (PYQ 2012) [1M] Ans: The speed of propagation i.e. c = 3 × 108 m/s we Electromagnetic Spectrum (PYQ 2020, 2019, 2018, 2016, 2015, 2014, 2011, 2010) The classification of electromagnetic waves according to their frequency is the electromagnetic spectrum. There is no sharp division between one kind of wave and next. The classification is based on how waves are produced and/or detected. Different types of electromagnetic waves- Type Wavelength Production Detection Uses range 1) Radio >0.1m Accelerated motion of charges Receiver’s ariels Radio and television waves in conducting wires communication systems. Cellular phones transmit voice signals in Ultrahigh frequency band (UHF). 2) Microwaves 0.1m to Klystron valves, Magnetron Point contact Radar systems in aircraft 1mm valve, Gunn diodes diodes navigation, used to time fast balls, tennis serves and automobiles. Microwave ovens in homes. 3) Infrared 1mm to Vibration of atoms and Thermopiles, IR lamps used in physical waves/ 700nm molecules in hot bodies bolometer, therapy, maintains Heat waves infrared earth’s avg temp. photographic film through greenhouse effect, IR detectors in satellites for military purpose and to observe growth of crops, LED’s emit IR waves and used in TV sets, video recorders and hi-fi systems  4) Light/ 700nm to Electrons in atoms emit light Eye, photocells, It enables us to see visible rays 400 nm when they move from a high photographic film things and provides energy level to a lower energy information about the level world 5) Ultraviolet 400nm to Inner shell electrons in atoms Photocells, Used in LASIK eye rays 1nm moving from one energy level photographic film surgery, UV lamps are to lower level used to kill germs in water purifiers 6) X- Rays 1nm to 10-3 Bombarding metals with high Photographic Used as a diagnostic tool nm energy electrons, X- Ray tubes, tubes, Geiger in detecting various inner shell electrons tubes, ionization forms of cancer chamber 7) Gamma