Physics Notes on Electromagnetism and Wave Interference

Electromagnetism and Interference/Diffraction Formulas

Electromagnetism

  • EMF=BLvsin(θ)EMF = BLv \sin(\theta)

    • Where:

      • EMFEMF is the electromotive force.

      • BB is the magnetic field strength.

      • LL is the length of the conductor in the magnetic field.

      • vv is the velocity of the conductor.

      • θ\theta is the angle between the velocity vector and the magnetic field vector.

  • P<em>AC=P</em>max</p><ul><li><p>ThisequationseemstorelatetopowerinanACcircuit,whereP<em>{AC} = P</em>{max}</p><ul><li><p>This equation seems to relate to power in an AC circuit, whereP{AC}mightrepresenttheaveragepowerandmight represent the average power andP{max}themaximumpower.</p></li></ul></li><li><p>the maximum power.</p></li></ul></li><li><p>\frac{VP}{VS} = \frac{NP}{NS},(Idealtransformer)</p><ul><li><p>Where:</p><ul><li><p>, (Ideal transformer)</p><ul><li><p>Where:</p><ul><li><p>V_Pisthevoltageintheprimarycoil.</p></li><li><p>is the voltage in the primary coil.</p></li><li><p>V_Sisthevoltageinthesecondarycoil.</p></li><li><p>is the voltage in the secondary coil.</p></li><li><p>N_Pisthenumberofturnsintheprimarycoil.</p></li><li><p>is the number of turns in the primary coil.</p></li><li><p>N_Sisthenumberofturnsinthesecondarycoil.</p></li></ul></li></ul></li></ul><h4id="7e77404fe9f4447f959fbb2e052220f1"datatocid="7e77404fe9f4447f959fbb2e052220f1"collapsed="false"seolevelmigrated="true">InterferenceandDiffraction</h4><h5id="7bdb3eead6bc4b199f27cc9006d370aa"datatocid="7bdb3eead6bc4b199f27cc9006d370aa"collapsed="false"seolevelmigrated="true">ConstructiveInterference</h5><ul><li><p>is the number of turns in the secondary coil.</p></li></ul></li></ul></li></ul><h4 id="7e77404f-e9f4-447f-959f-bb2e052220f1" data-toc-id="7e77404f-e9f4-447f-959f-bb2e052220f1" collapsed="false" seolevelmigrated="true">Interference and Diffraction</h4><h5 id="7bdb3eea-d6bc-4b19-9f27-cc9006d370aa" data-toc-id="7bdb3eea-d6bc-4b19-9f27-cc9006d370aa" collapsed="false" seolevelmigrated="true">Constructive Interference</h5><ul><li><p>2d = m\lambda_{film},where, wherem = 0, 1, 2, …</p><ul><li><p>Occurswhentwowavesareeitherbothinvertedornoneareinverted.</p></li><li><p></p><ul><li><p>Occurs when two waves are either both inverted or none are inverted.</p></li><li><p>disthethicknessofthefilm.</p></li><li><p>is the thickness of the film.</p></li><li><p>\lambda_{film}isthewavelengthoflightinthefilm.</p></li><li><p>is the wavelength of light in the film.</p></li><li><p>misanintegerrepresentingtheorderoftheinterference.</p></li></ul></li></ul><h5id="05b98f2c41934116ac6993032ba730ef"datatocid="05b98f2c41934116ac6993032ba730ef"collapsed="false"seolevelmigrated="true">DestructiveInterference</h5><ul><li><p>is an integer representing the order of the interference.</p></li></ul></li></ul><h5 id="05b98f2c-4193-4116-ac69-93032ba730ef" data-toc-id="05b98f2c-4193-4116-ac69-93032ba730ef" collapsed="false" seolevelmigrated="true">Destructive Interference</h5><ul><li><p>2d = (m + \frac{1}{2})\lambda_{film},where, wherem = 0, 1, 2, …</p><ul><li><p>Occurswhenonewaveisinverted.</p></li></ul></li></ul><h5id="4a07d393b5b847c3bc4ff8e0528048ae"datatocid="4a07d393b5b847c3bc4ff8e0528048ae"collapsed="false"seolevelmigrated="true">Generalformulasforinterference</h5><ul><li><p>Whenthefilmisinavacuum:</p><ul><li><p>Occurs when one wave is inverted.</p></li></ul></li></ul><h5 id="4a07d393-b5b8-47c3-bc4f-f8e0528048ae" data-toc-id="4a07d393-b5b8-47c3-bc4f-f8e0528048ae" collapsed="false" seolevelmigrated="true">General formulas for interference</h5><ul><li><p>When the film is in a vacuum:\lambda{film} = \lambda{vacuum}</p></li><li><p>Generalformulasforinterference(EitherbothwavesORnoneareinverted):</p><ul><li><p></p></li><li><p>General formulas for interference (Either both waves OR none are inverted):</p><ul><li><p>2d = m\lambda_{film},where, wherem = 1, 2, 3, …</p></li><li><p></p></li><li><p>2d = (m + \frac{1}{2})\lambda_{film},where, wherem = 0, 1, 2, …</p></li></ul></li></ul><h4id="b2f59b5bb77c4e2dbb58591ee0787ac2"datatocid="b2f59b5bb77c4e2dbb58591ee0787ac2"collapsed="false"seolevelmigrated="true">Constants</h4><ul><li><p>Speedoflight:</p></li></ul></li></ul><h4 id="b2f59b5b-b77c-4e2d-bb58-591ee0787ac2" data-toc-id="b2f59b5b-b77c-4e2d-bb58-591ee0787ac2" collapsed="false" seolevelmigrated="true">Constants</h4><ul><li><p>Speed of light:c = 3 \times 10^8 m/s</p></li><li><p>Accelerationduetogravity:</p></li><li><p>Acceleration due to gravity:g = 9.81 m/s^2</p></li></ul><divdatatype="horizontalRule"><hr></div><h4id="a448560e9e3f42fe9df34e7649b6e13e"datatocid="a448560e9e3f42fe9df34e7649b6e13e"collapsed="false"seolevelmigrated="true">RotatingCoilinMagneticField</h4><ul><li><p>Figure(a)showsacircularcoilimmersedinaregularmagneticfieldperpendiculartothecoilssurface.</p></li><li><p>Figure(b)showsthecoilbeingrotatedinthemagneticfield.</p></li><li><p>Question:WhathappenswhenthecoilisrotatedinthemagneticfieldfromthepositioninFigure(a)tothepositioninFigure(b)?</p></li></ul><h4id="d02820b28d7f4c4193175adaedbdbc95"datatocid="d02820b28d7f4c4193175adaedbdbc95"collapsed="false"seolevelmigrated="true">MagnetsandWire</h4><ul><li><p>Figure(1)showstwomagnetswiththenorthpole(N)ofthefirstmagnetfacingthesouthpole(S)ofthesecondmagnet.</p></li><li><p>Thelengthofeachmagnetis</p></li></ul><div data-type="horizontalRule"><hr></div><h4 id="a448560e-9e3f-42fe-9df3-4e7649b6e13e" data-toc-id="a448560e-9e3f-42fe-9df3-4e7649b6e13e" collapsed="false" seolevelmigrated="true">Rotating Coil in Magnetic Field</h4><ul><li><p>Figure (a) shows a circular coil immersed in a regular magnetic field perpendicular to the coil's surface.</p></li><li><p>Figure (b) shows the coil being rotated in the magnetic field.</p></li><li><p>Question: What happens when the coil is rotated in the magnetic field from the position in Figure (a) to the position in Figure (b)?</p></li></ul><h4 id="d02820b2-8d7f-4c41-9317-5adaedbdbc95" data-toc-id="d02820b2-8d7f-4c41-9317-5adaedbdbc95" collapsed="false" seolevelmigrated="true">Magnets and Wire</h4><ul><li><p>Figure (1) shows two magnets with the north pole (N) of the first magnet facing the south pole (S) of the second magnet.</p></li><li><p>The length of each magnet isl = 20.0 cmandtheheightisand the height ish = 6.00 cm.</p></li><li><p>Auniformmagneticfieldofstrength.</p></li><li><p>A uniform magnetic field of strengthB = 54 mTexistsbetweenthemagnets.</p></li><li><p>Atautwireconnectedtoamilliammeterismovedfromthelowerendofthemagnetstotheupperend,perpendiculartothemagneticfieldlines,inatimeperiodofexists between the magnets.</p></li><li><p>A taut wire connected to a milli-ammeter is moved from the lower end of the magnets to the upper end, perpendicular to the magnetic field lines, in a time period of\Delta t = 0.2 s(Figure2).</p></li></ul><h5id="5c2e6beb4be74facb39ab56ca8db5773"datatocid="5c2e6beb4be74facb39ab56ca8db5773"collapsed="false"seolevelmigrated="true">Calculations</h5><p>a)Theinducedelectromotiveforce(EMF)generatedinthewire.<br>b)Theinducedelectriccurrentpassinginmilliammeter,iftheelectricalresistanceofthecircuitis(Figure 2).</p></li></ul><h5 id="5c2e6beb-4be7-4fac-b39a-b56ca8db5773" data-toc-id="5c2e6beb-4be7-4fac-b39a-b56ca8db5773" collapsed="false" seolevelmigrated="true">Calculations</h5><p>a) The induced electromotive force (EMF) generated in the wire.<br>b) The induced electric current passing in milli-ammeter, if the electrical resistance of the circuit is2.0 \Omega.</p><divdatatype="horizontalRule"><hr></div><h4id="489ad3ca98484f56bb4df3b1c43b7957"datatocid="489ad3ca98484f56bb4df3b1c43b7957"collapsed="false"seolevelmigrated="true">HairDryerandPotentialDifference</h4><p>A.Amanufacturedhairdryeruses.</p><div data-type="horizontalRule"><hr></div><h4 id="489ad3ca-9848-4f56-bb4d-f3b1c43b7957" data-toc-id="489ad3ca-9848-4f56-bb4d-f3b1c43b7957" collapsed="false" seolevelmigrated="true">Hair Dryer and Potential Difference</h4><p>A. A manufactured hair dryer uses10 Aatat120 V.Ifthedryerisusedinanothercountrywherethepotentialdifferenceis. If the dryer is used in another country where the potential difference is240 V.</p><h5id="2ea5431929df454ebc1049b2224b8f0e"datatocid="2ea5431929df454ebc1049b2224b8f0e"collapsed="false"seolevelmigrated="true">Questions:</h5><p>a)Whattool/deviceenablesustouseahairdryer,whenmovingbetweentwocountrieswithdifferentpotentialdifferences(Voltagesources)?<br>b)Findtheratioofthenumberofturnsintheprimarycoiltothenumberofturnsinthesecondarycoil.<br>c)Findthevalueofcurrentthatthehairdryerdrawsfromthe.</p><h5 id="2ea54319-29df-454e-bc10-49b2224b8f0e" data-toc-id="2ea54319-29df-454e-bc10-49b2224b8f0e" collapsed="false" seolevelmigrated="true">Questions:</h5><p>a) What tool / device enables us to use a hair dryer, when moving between two countries with different potential differences (Voltage sources)?<br>b) Find the ratio of the number of turns in the primary coil to the number of turns in the secondary coil.<br>c) Find the value of current that the hair dryer draws from the240 Vline?</p><h4id="0d444a2e26514e10a2545d5d0bf25e1b"datatocid="0d444a2e26514e10a2545d5d0bf25e1b"collapsed="false"seolevelmigrated="true">Transformers</h4><p>B.Thetablecontainstherelationshipsbetweenpotentialdifference(V),current(I),andthenumberofwindingsintransformers(N)intheprimary(P)andsecondary(S)windings.</p><h5id="575eed587e344417a0ba24844c18f754"datatocid="575eed587e344417a0ba24844c18f754"collapsed="false"seolevelmigrated="true">StepUpTransformer</h5><p>Studytheinequalitiesinthetableandshowtherelationshipsbetweenthequantitiesinthestepuptransformerandthestepdowntransformer,byplacingthemathematicalsymbols(line?</p><h4 id="0d444a2e-2651-4e10-a254-5d5d0bf25e1b" data-toc-id="0d444a2e-2651-4e10-a254-5d5d0bf25e1b" collapsed="false" seolevelmigrated="true">Transformers</h4><p>B. The table contains the relationships between potential difference (V), current (I), and the number of windings in transformers (N) in the primary (P) and secondary (S) windings.</p><h5 id="575eed58-7e34-4417-a0ba-24844c18f754" data-toc-id="575eed58-7e34-4417-a0ba-24844c18f754" collapsed="false" seolevelmigrated="true">Step-Up Transformer</h5><p>Study the inequalities in the table and show the relationships between the quantities in the step-up transformer and the step-down transformer, by placing the mathematical symbols (>, <, =)correctly.</p><h5id="ca3ad526d1cf419fab3bbd32e19f45e6"datatocid="ca3ad526d1cf419fab3bbd32e19f45e6"collapsed="false"seolevelmigrated="true">StepDownTransformer</h5><h4id="1a3ac8bf199e489ead69d6994222ca50"datatocid="1a3ac8bf199e489ead69d6994222ca50"collapsed="false"seolevelmigrated="true">MagnetandCoil</h4><p>A.Thenorthpoleofamagnetapproachesacoil,andthemilliammeterindicatorconnectedtoitmoves.Thefigureshowsasideviewofthemagnetasitapproachesthecoil.</p><h5id="3594fb6b45be4657823cc3fb0210627e"datatocid="3594fb6b45be4657823cc3fb0210627e"collapsed="false"seolevelmigrated="true">Question</h5><p>Determinethedirectionoftheinducedelectriccurrentgeneratedinthecoil,andexplainhowyougottheanswer(statethelawyoureliedontodeterminethis).</p><h4id="daf7e7ebeb994a8e80f4ec3342ebd8c0"datatocid="daf7e7ebeb994a8e80f4ec3342ebd8c0"collapsed="false"seolevelmigrated="true">LightSourcesandDoubleSlitExperiment</h4><p>B.Aretwolightsources,onegreenandtheotherred,coherent,orincoherent?Explainyouranswer.</p><p>C.AtopviewofthedoubleslitinvestigationisshowninFigure.Thewavefrontsinterfereconstructivelyanddestructivelytoformapatternoflightanddarkbands.</p><h5id="8f79703b33f94fcf8968f56ab3515ae6"datatocid="8f79703b33f94fcf8968f56ab3515ae6"collapsed="false"seolevelmigrated="true">Questions</h5><ol><li><p>Determinethetypeofinterferenceineachofthetwofiguresshownbelow?Markthebandthatproducesadarkband.</p></li></ol><divdatatype="horizontalRule"><hr></div><h4id="18d43de45c8b4a22a1c9487ec9ffdc56"datatocid="18d43de45c8b4a22a1c9487ec9ffdc56"collapsed="false"seolevelmigrated="true">YoungsDoubleSlitExperiment</h4><p>A.Youngsdoubleslitexperimentcanbeusedtomeasurethewavelengthofagivenlight.Inthefigurebelow,theslitsare) correctly.</p><h5 id="ca3ad526-d1cf-419f-ab3b-bd32e19f45e6" data-toc-id="ca3ad526-d1cf-419f-ab3b-bd32e19f45e6" collapsed="false" seolevelmigrated="true">Step-Down Transformer</h5><h4 id="1a3ac8bf-199e-489e-ad69-d6994222ca50" data-toc-id="1a3ac8bf-199e-489e-ad69-d6994222ca50" collapsed="false" seolevelmigrated="true">Magnet and Coil</h4><p>A. The north pole of a magnet approaches a coil, and the milli-ammeter indicator connected to it moves. The figure shows a side view of the magnet as it approaches the coil.</p><h5 id="3594fb6b-45be-4657-823c-c3fb0210627e" data-toc-id="3594fb6b-45be-4657-823c-c3fb0210627e" collapsed="false" seolevelmigrated="true">Question</h5><p>Determine the direction of the induced electric current generated in the coil, and explain how you got the answer (state the law you relied on to determine this).</p><h4 id="daf7e7eb-eb99-4a8e-80f4-ec3342ebd8c0" data-toc-id="daf7e7eb-eb99-4a8e-80f4-ec3342ebd8c0" collapsed="false" seolevelmigrated="true">Light Sources and Double-Slit Experiment</h4><p>B. Are two light sources, one green and the other red, coherent, or incoherent? Explain your answer.</p><p>C. A top view of the double-slit investigation is shown in Figure. The wavefronts interfere constructively and destructively to form a pattern of light and dark bands.</p><h5 id="8f79703b-33f9-4fcf-8968-f56ab3515ae6" data-toc-id="8f79703b-33f9-4fcf-8968-f56ab3515ae6" collapsed="false" seolevelmigrated="true">Questions</h5><ol><li><p>Determine the type of interference in each of the two figures shown below? Mark the band that produces a dark band.</p></li></ol><div data-type="horizontalRule"><hr></div><h4 id="18d43de4-5c8b-4a22-a1c9-487ec9ffdc56" data-toc-id="18d43de4-5c8b-4a22-a1c9-487ec9ffdc56" collapsed="false" seolevelmigrated="true">Young's Double-Slit Experiment</h4><p>A. Young's double-slit experiment can be used to measure the wavelength of a given light. In the figure below, the slits are1.90 \times 10^{-5} mapart,ascreenisplacedapart, a screen is placed0.60 maway,andthefirstorderbrightbandisaway, and the first order bright band is2.11 \times 10^{-2} mfromthecentralbrightband.</p><h5id="e7a2456059f349f19e8cf7ba6f007367"datatocid="e7a2456059f349f19e8cf7ba6f007367"collapsed="false"seolevelmigrated="true">Questions</h5><p>a)Calculatethewavelengthofredlight.<br>b)Whathappenstotheintensityofthebrightbandsaswemoveawayfromthecentralband?<br>c)Whatwouldhappenifwhitelightwasusedinsteadofred?</p><h4id="48128e004828403da51c8d1c2d11989e"datatocid="48128e004828403da51c8d1c2d11989e"collapsed="false"seolevelmigrated="true">OilSlickandInterference</h4><p>B.Youobservecoloredringsonapuddleandconcludethattheremustbeanoilslickonthewater.Youlookdirectlydownthepuddleandseeayellowgreenregion(from the central bright band.</p><h5 id="e7a24560-59f3-49f1-9e8c-f7ba6f007367" data-toc-id="e7a24560-59f3-49f1-9e8c-f7ba6f007367" collapsed="false" seolevelmigrated="true">Questions</h5><p>a) Calculate the wavelength of red light.<br>b) What happens to the intensity of the bright bands as we move away from the central band?<br>c) What would happen if white light was used instead of red?</p><h4 id="48128e00-4828-403d-a51c-8d1c2d11989e" data-toc-id="48128e00-4828-403d-a51c-8d1c2d11989e" collapsed="false" seolevelmigrated="true">Oil Slick and Interference</h4><p>B. You observe colored rings on a puddle and conclude that there must be an oil slick on the water. You look directly down the puddle and see a yellow green region (\lambda = 555 nm),If), If(n{oil} = 1.45)andand(n{water} = 1.33).</p><h5id="9e876d3f17904d5fad0e69f4414560fe"datatocid="9e876d3f17904d5fad0e69f4414560fe"collapsed="false"seolevelmigrated="true">Questions</h5><p>a)Determineinthefollowingtable,whathappenstothewave(wavephase)whenitisreflectedfromeachofthetwosurfaces:(airoil)and(oilwater),byplacingasign(.</p><h5 id="9e876d3f-1790-4d5f-ad0e-69f4414560fe" data-toc-id="9e876d3f-1790-4d5f-ad0e-69f4414560fe" collapsed="false" seolevelmigrated="true">Questions</h5><p>a) Determine in the following table, what happens to the wave (wave phase) when it is reflected from each of the two surfaces: (air-oil) and (oil water), by placing a sign (\checkmark$$) in the appropriate box:

    Inversion

    No inversion

    air-oil

    oil-water

    b) Find the minimum thickness of oil that could cause this color.