Electromagnetic Waves

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Darren Day
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1 Eectromagnetic Waves Dispacement Current- It is that current that comes into existence (in addition to conduction current) whenever the eectric fied and hence the eectric fux changes with time. It is equa to ϵ times the rate of change of eectric fux through a given surface. I D de dt Need of Dispacement Current- (1) An exampe iustrating the need for dispacement current arises in connection with capacitors with no medium between the pates. It is found that during the charging of a capacitor a magnetic fied exist in vacuum between the pates athough there is no actua transportation of charge from one pate to another. The expanation is that a dispacement current fow in vacuum and this current produces the magnetic fied in the region between the pates. (2) To expain the Inconsistency of Ampere s aw- Let us consider the case of a charging parae pate capacitor and appying the Ampere s circuita aw for surfaces L and R. For surface R, B. d For surface L, B. d 1 P a g e I Since L and R are the surfaces of same oop so there is an apparent contradiction in appying Ampere s aw in this case. Maxwe resoves the above inconsistency by introducing the concept of dispacement current. Dispacement current- The eectric fied between the pates of a parae pate capacitor is given as Q / A Q E A Q EA Q E Taking the differentia on the both sides- dq de dt dt de I D dt de Thus is mathematicay equivaent current for surface L to the conduction current I, dt which pierces surface R. This effective current is caed as dispacement current and it is

defined as the current which appears in the region where eectric fied (and hence eectric fux) is changing with time. Important properties of dispacement current- 1.

The magnitude of dispacement current is equa to the rate of dispacement of charge from one pate to other pate of a capacitor. 4.

2 defined as the current which appears in the region where eectric fied (and hence eectric fux) is changing with time. Important properties of dispacement current- 1. Dispacement current exists whenever there is a change of eectric fux. 2. It ony adds to current density in Ampere s circuita aw. As it produces magnetic fied so it is caed a current. 3. The magnitude of dispacement current is equa to the rate of dispacement of charge from one pate to other pate of a capacitor. 4. Together with the conduction current, dispacement current satisfies the property of continuity. Ampere Maxwe s Law-This is the modified form of ampere s circuita aw and according to this aw The ine integra of magnetic fied over a cosed oop is μ times the sum of conduction current and dispacement current. i. e. B. d ( I I ) B. d = I C C D de dt Eectromagnetic Waves- A wave radiated by an acceerated charge partice, propagating through space as couped eectric and magnetic fieds, osciating perpendicuary to each other and to the direction of propagation of the wave, is caed Eectromagnetic Wave. OR Eectromagnetic waves consist of sinusoida variation of eectric and magnetic fieds at right anges to each other and to the direction of propagation of wave. Mathematica representation of eectromagnetic waves- Adjacent figure shows a pane em wave of frequency ν and waveength λ traveing aong x- axis with speed c. The eectric fied E Osciates aong y axis and magnetic fied B osciates aong z- axis. The eectric fied can be written as- x E Ey j Esin( kx t) j Esin 2 vt j x t E E sin 2 j (1) T 2 P a g e

3 Where k 2 / is the propagation constant and anguar frequency, 2 The magnetic fied vector can be written as- x B Bz k Bsin( kx t) k Bsin 2 vt k x t B B sin 2 k (2) T Here E and B are the ampitudes of the eectric fied and magnetic fied respectivey and they reated as E c B Thus, from equations (1) and (2) show that the variations in eectric and magnetic fieds are in same phase. Transverse Nature of Eectromagnetic Waves- Suppose a pane EMW is traveing in +X direction. Consider cube with sides parae to the coordinate axis as shown in diagram. For the situation we are considering (i. e. no charges or on conduction currents), the eectric fux or magnetic fux through this cube is zero. According to Gauss s theorem the eectric fux through this surface is given as- S E. ds Q Y P O R B C E E 2 1 X A D There is no contribution to net eectric fux from the top and bottom or from the front and back faces of the cube because pane wave depend ony on x and t. Z Fux through the eft face, L EA 1 Fux through the right face R EA 2 Net fux, R L E2A E1A = (E 2 E 1 ) A= Since A (area) can t be zero) so E 1 - E 2 = Now there are two possibiities viz., either E 1 = E 2 or E 1 = E 2 =. In case E 1 = E 2, it woud mean that eectric fied associated with EMW is constant. But such a constant fied cannot give rise to a wave. Therefore E 1 = E 2 = i.e. there is no eectric fied in the direction of wave propagation. Simiar reason can be appied for magnetic fied. 3 P a g e

4 Thus Eectric fied and magnetic fied associated with EM waves are transverse to the direction of propagation. Maxwe s Equation- Maxwe s four equations describe the eectric and magnetic fieds arising from varying distributions of eectric charges and currents, and how those fieds change in time. 1. Gauss Law for eectric fieds: q E. ds (The integra of the outgoing eectric fied over an area encosing a voume equas the tota charge inside.) 2. According to Gauss s Theorem in magnetism, the surface integra of magnetic fied over a cosed surface is aways zero i.e. B. ds= (No magnetic charge exists: no monopoes ). B 3. Faraday s Law of Magnetic Induction: E. d The first term is integrated round S a cosed ine, usuay a wire, and gives the tota votage change around the circuit, which is generated by a varying magnetic fied threading through the circuit. d dt 4. Ampere s Law pus Maxwe s dispacement current: de B. d = I C dt This gives the tota magnetic force around a circuit in terms of the current through the circuit, pus any varying eectric fied through the circuit (that s the dispacement current ). Characteristic Properties of EMW- 1. Eectromagnetic waves are propagated by osciating eectric and magnetic fieds osciating at right anges to each other i.e. acceerating charge partice is the source of EMW. 2. Eectromagnetic waves trave with a constant veocity of 3 x 1 8 m/s in vacuum The speed of EMW in vacuum is given by c and in a medium v 4. Eectromagnetic waves are not defected by eectric or magnetic fied. 5. Eectromagnetic waves can show interference or diffraction. 6. Eectromagnetic waves are transverse waves. 7. Eectromagnetic waves may be poarized. Eectromagnetic waves need no medium for propagation. 8. The energy from the sun is received by the earth through eectromagnetic waves. 9. The optica effect of EMW is due to eectric fied vector. 1. The waveength (λ) and the frequency (v) of eectromagnetic wave is reated as c = νλ = ω/k. where k is propagation constant and k=2π/λ. 11. Eectromagnetic radiations act as waves as we as photons (partice) having no mass. 12. The frequency of the waves remains same when they change medium during transmission. 4 P a g e

5 13. Eectromagnetic waves are waves of fieds and not of matter as are waves on water or rope. 14. Eectromagnetic waves carry momentum and exert the force and hence a pressure on the surface at which they incident. The eectromagnetic waves transport inear momentum as they trave through space: U p c 15. The eectromagnetic waves carry energy as they trave through space and this energy is shared equay by eectric and magnetic fieds. The average energy density of e. m. wave is 1 B u ue ub E 2 Eectromagnetic Spectrum- 2 2 The ordery arrangement of eectromagnetic wave according to their waveength of frequency is caed as the eectromagnetic spectrum. 5 P a g e

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7 Different Parts of EM Spectrum and their main uses- (1) Radio waves. Radio waves are produced by the acceerated motion of charges in conducting wires, and are used in radio and teevision communication systems. Frequency range of radio waves is generay from 5 khz to about 1 MHz (2) Microwaves. Microwaves (short-waveength radio waves), have frequencies in the gigahertz (GHz) range. They are produced by specia vacuum tubes (caed kystrons, magnetrons and Gunn diodes). Main uses (i) RADAR (Radio Detection and Ranging)- Radar is used for aircraft navigation. Because of smaer waveengths, radar can be directed as a beam signa in any direction. Radar aso provides basis to determine the speeds of fast moving objects ike tennis serves and automobies etc. (ii) Microwave Ovens- The frequency of the microwaves is matched with the resonant frequency of water moecues which transfers energy from the microwaves to the water moecues as Kinetic Energy. This raises the temperature of the food containing water. Meta containers are not used in microwave ovens due to foowing reasons: (a) Danger of getting a shock from accumuated eectric charges. (b) Metas may aso met from the intense heating. Porceain containers are used-because its moecues vibrate with much smaer frequencies and thus cannot absorb microwaves. Hence they do not get heated up. (3) Infrared Waves (Heat Waves). Infrared waves get produced by moecues of hot bodies and are aso referred to as heat waves. Main uses- (i) In physica therapy - for giving warmth to the afficted part of the body (IR bubs). (ii) In maintaining earth warm through the greenhouse effect (detaied out a itte ater). (m) Infra-red detectors are used in sateites for miitary purposes as we as to observe growths of crops. (iv) LEDs emit infrared radiations. They are used in remote contro switches as in TV sets. (4) Visibe Waves (Light Waves):- It is the part of the spectrum that is detected by the human eye. It has the frequency range from about 4 x 114 Hz to about 7 x114 Hz or a wave-ength range of about 7 4 nm. Our eyes are sensitive to this range of waveengths. (5) Utravioet Waves (UV Waves) - UV rays range from about 4 x 1-7 m (4 nm) to 6 x 1-1 m (.6 nm). UV radiation is produced by specia amps and very hot bodies. Most of the U.V. radiation from sun is absorbed in the ozone ayer in the atmosphere. UV ight has harmfu effects on humans. Exposure to UV radiation causes the production of more meanin in the body, resuting in the tanning of the skin. 7 P a g e

8 UV radiation is absorbed by ordinary gass. Hence, one cannot get tan or sunburn through gass window. Weders wear specia gasses or face masks with gass windows to protect their eyes from arge amount of UV produced by weding arcs.. Main Uses - (i) LASIK (Laser Assisted in Situ Keratomieusis) Eye Surgery. Since UV radiation has very short waveength, they can be focused for high precision surgica appications. (ii) UV amps are use/d to ki germs in water purifiers and for food-preservation. (iii) Treatment of skin compaints. (iv) Fuorescent ighting. (v) Burgar aarms. (vi) Automatic counting in industry. (7) X-Rays- Higher than UV frequencies ies the X-ray region. It covers waveengths from about 1-8 m (1 nm) down to 1-13 m (14 nm). The common way to generate X-rays is to bombard a meta target by high energy eectrons. Main uses- (i) To find out fractures in bones, position of bones, impacted teeth etc. (ii) Radiography (iii) Radioogy. (iv) Detecting faws in metas. (v) Diffraction to find crysta structure. (vi) Detection of art forgeries. Note: Over-exposure of X-rays can be harmfu. (8) Gamma Rays- Gamma rays ie in the upper most frequency range of the e.m. spectrum. They have wave engths from about 1-1m to ess than 1-14m. They are produced in nucear reactions and aso emitted by radioactive nucei. Main uses - (i) To carry out nucear reactions. (ii) They have the highest frequencies, hence highest penetrating power. (m) To detect faws in meta castings. (iv) Steriization. (v) Medicina uses e.g. Cancer treatment. (9) Roe of ozone ayer- E.M. radiations having UV and higher frequencies cause genetic damage to iving ces. The ozone ayer bocks the passage of UV radiations and effectivey protects us from the harmfu portions of soar radiations. (1) Greenhouse effect- Energy from sun heats the earth. As earth's surface temperature remains ow, the radiations being emitted by earth are mosty in the infrared region. These radiations do not escape earth whose atmosphere pus ow ying couds refect them back. This keeps earth's surface warm. This is caed greenhouse effect. 8 P a g e

Gauss Law. 2. Gauss s Law: connects charge and field 3. Applications of Gauss s Law

Gauss Law. 2. Gauss s Law: connects charge and field 3. Applications of Gauss s Law Gauss Law 1. Review on 1) Couomb s Law (charge and force) 2) Eectric Fied (fied and force) 2. Gauss s Law: connects charge and fied 3. Appications of Gauss s Law Couomb s Law and Eectric Fied Couomb s