20 Overview current  magnetic field magnetic field  current current  magnetic field magnetic field  current Laws of Faraday & Lenz transformers & power transmission Homework: 4, 9, 15, 19, 26, 45, 55, 69, 78.

Motional EMF magnetic force on free charges creates voltage across rod magnetic force on free charges creates voltage across rod qE = qvB E = vB EL = vBL emf = vBL

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.

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

Lenz’s Law induced voltage opposes the change which produced it 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

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.

Applications of Faraday’s Law Pick up coils Generators

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.

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

Chapter Summary moving conductor in a B field gets a motional emf. 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 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

Direct Current (DC) Generators split ring keeps current flowing in only one direction output can be smoothed

Increased by a factor of 50 It is the same Not enough information 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

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