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0. 20 Overview. current magnetic field magnetic field current Laws of Faraday & Lenz transformers & power transmission Homework: 4, 9, 15, 19, 26, 45, 55, 69, 78. 0. Motional EMF. magnetic force on free charges creates voltage across rod qE = qvB E = vB EL = vBL

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## 20 Overview

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**0**20 Overview • current magnetic field • magnetic field current • Laws of Faraday & Lenz • transformers & power transmission • Homework: • 4, 9, 15, 19, 26, 45, 55, 69, 78.**0**Motional EMF • magnetic force on free charges creates voltage across rod • qE = qvB • E = vB • EL = vBL • emf = vBL**0**A (d = 1m) bar moves (v = 20 m/s) as shown. (B = 0.25 T). Calculate the emf and the current in the resistor (R = 5.0 Ω).**Magnetic Flux**• Motional emf works for straight wires, but not for loops • Solution: Magnetic Flux Concept • Faraday’s Law: Voltage induced in loop equals the _______ the Magnetic Flux • ______________. • Magnetic Flux is a field x area product • Unit: T·m2**Magnetic Flux Concept**• Method: Draw field lines & loop • Flux is the # lines passing thru loop • Draw the change • Voltage ~ rate of change in # lines thru loop**Calculating B-Flux**Ex. B = 1.0T, Area = 10. sq.m., angle = 30 degrees.**0**Faraday’s Law (1 T·m2 /s = 1 volt) N is number of turns of wire on loop. Ex. 50 turns of wire has:**What motions produce a change in flux thru the single loop?**If the single loop is moved to the right, what is the direction of the current induced in it?**Which of the following can produce a changing magnetic flux?**• B change • Area change • angle change • none of these • all of these**0**Lenz’s Law • induced voltage opposes the change which produced it • Ex: A magnet moving in or out of a coil feels a magnetic force which opposes the motion of the magnet • Ex. Lenz Law Tube**0**Ex. A 1.0 sq.m. loop has 60 turns. Its normal is parallel to a uniform B-field of strength 0.10 T. It is rotated so its normal is perpendicular to B in a time of 1.0s. Calculate the voltage induced.**0**Applications of Faraday’s Law • Pick up coils • Generators**0**Alternating Current (AC) Generators • Coil rotates at ω = θ/t (θ = ωt) • Rotation flux change • Voltage = NBAωsin(ωt)**a) What must be the magnetic field strength so that a**generator consisting of 1000 turns of a coil of radius 25 cm produces a peak output of 160 V when turned at a frequency of 60 Hz? b) Sketch a graph of the output of the generator. 0**Transformers**• Flux & ΔΦB/Δt _________ for each coil • By Faraday’s Law: • Vp = Np ΔΦB/Δt and • Vs = Ns ΔΦB/Δt**Power and Current in Transformers**• Conservation of Energy implies power at primary is the same as power at secondary: • ______________ • Ex: A transformer increases voltage by a factor of ten, the output (secondary) current decreases by a factor of ten:**Electromagnetic Waves**• Faraday: time varying B produces time varying E • Maxwell: time varying E produces time varying B • i.e. one begets the other & self-sustaining, time-varying EM wave is produced**Polarization**• overall orientation of electric field of light • simplest cases: unpolarized (radial), plane polarized (linear)**Polarizing Filters**• Polarizing material allows the passage of only one direction of E • Malus’ Law:**Properties of Electromagnetic Waves**• travel in vacuum • transverse waves • speed in a vacuum governed by magnetic and electric constants of free space • c = fl = 299,792,458 m/s (3.00 x 108 m/s)**Spectrum by Wavelength**• microwaves: cm range waves strongly absorbed by water. cold spots separated by half-wavelength • infrared (IR): ~mm to um waves also strongly absorbed by water • radio waves: wavelengths ~ 1 to 500 meters • Ex. f = 100 MHz. What is its wavelength? • visible: ~ 400 to 700 nm (400 is violet, 700 is red) • ultraviolet (UV): ~ 0.1 to 100 nm, causes sunburn • x-ray: ~ 0.01 to 0.001 nm waves can pass through 10cm of many materials • gamma-rays: < 0.001 nm waves are even more penetrating**Standing Waves**• Confined microwaves create a standing wave • Hot spots are separated by half a wavelength • Most microwave ovens are around 2400MHz**0**Chapter Summary • moving conductor in a B field gets a motional emf. • Faraday’s Law: emf = -DF/Dt • Lenz’s Law: energy conservation • generators & motors utilize F = ILB, experience back emf • transformers step ac voltages up or down • EM waves: E & B oscillation**Intensity**• wave intensity in watts/square-meter: • Ex. 5 mW laser is focused to a spot size of diameter 1.0 mm.**Intensity for Different Types of Waves**• Plane Waves – Intensity is constant • Spherical Waves – Intensity falls off as inverse square**Energy in EM Waves**• E = cB • u = ε0 E2 = (1/μ0)B2 • Intensity S = cu = cε0E2 = (c/μ0)B2**Ex. A laser beam has a peak intensity of 150 W/m2. Find**the amplitude of the electric and magnetic fields. • S = cu = cε0E2 = (c/μ0)B2**Eddy Currents**• Current induced in metal due to magnetic fields**calculating emf for loops**• summary: • draw magnetic field lines • count the number of penetrating lines (# that pass through the loop) at two (or more) times • the emf induced is ~ to the change in # of penetrating lines per second • # penetrating lines ~ “magnetic flux”**A metallic wire loop is in a uniform magnetic field.**• How does the flux change if: • ring moves a little to left or right? • ring begins to rotate?**Producing B and E Fields**• Electrical current creates B • Changing B field creates a circulating E field. • This E field creates the circulating currents observed in wire loops.**Back emf**• rotating coil in motor experiences an induced emf opposite to battery’s V • net voltage = V – back-emf = IR • I = current in motor • R = resistance of motor coil • back-emf ~ speed of coil, therefore is zero when motor starts (or freezes) • current is large when back-emf is small**0**Direct Current (DC) Generators • split ring keeps current flowing in only one direction • output can be smoothed**120 V ac is applied across the primary of a step down**transformer with turns ratio 1/50. How does the power applied at the primary compare to that at the secondary? (Assume a lossless transformer) • Reduced by a factor of 50 • Increased by a factor of 50 • It is the same • Not enough information**0**Application to Power Generation • Higher voltage transmission reduces resistive heat loss (I2R). • Ex. Power transmitted thru 10m long wire which has 1 ohm resistance. • At 6V: Current = V/R = 6V/1ohm = 6A • At 60V: Current = V/R = 60V/1ohm = 6A

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