Huiswerk Hoofstuk 30 Chapter 30 Homework

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1 Huiswerk Hoofstuk 30 Chapter 30 Homework 8 th /8 de th / 9 ste

2 Elektriese Induksie Twee Eksperimente Chapter 30 Electrical Induction Two Experiments Current loop + Magnetic field Torque Stroom in lus + magneetveld draaimoment Electric / Elektriese motor Torque + Magnetic field Current? Draai-moment + magneetveld Stroom? Faraday s Law of induction/ Wet van induksie Electric generator/ Elektriese Opwekker 2

3 Eksperiment 1 Experiment 1 Geen battery of emk bron Geen stroom aanvanklik Beweeg magneet t.o.v. lus stroom in lus. Stop magneet geen stroom Magneet beweeg in teenoorgestelde rigting stroom vloei in teenoorgestelde rigting No battery or emf source No current initially Move magnet w.r.t loop current appears. Magnet stops current stops Magnet moves opposite direction current flows opposite direction Beweeg vinniger grootter stroom Gebruik N of S pole bepaal stroom rigting Move faster greater current Using N or S poles determines current direction Geïnduseerde stroom Geïnduseerde emk W/q Proses = Induksie Induced current Induced emf W/q Process = Induction 3

4 Eksperiment 2 Experiment 2 Twee geleidende lusse. Naby mekaar maar raak nie 2 Conducting loops. Close together not touching Maak skakelaar S toe Stroom begin vloei Regterkant Vir n oomblik stroom in linkerkank ook. Ge-induseerde stroom Maak skakelaar S oop Vir n oomblik stroom in linkerkank ook. Ge-induseerde stroom net wanneer die stroom verander nie wanneer dit konstant is Close switch S Current starts to flow Right For a moment current on left as well. Induced current Open switch S For a moment current on left as well. Induced current only when current is changing not when it is constant. 4

5 30-3 Faraday se wet van Induksie Grootte van magneetveld maak nie saak - geinduseerde emk bepaal deur tempo van verandering in magnetiese vloed. In Hf 24 - Vloed Hoeveelheid B deur lus Φ Φ Faraday se wet: Grootte van emk E geinduseer in geleidende lus is gelyk aan die tempo waarteen die magnetiese vloed Φ B deur die lus verander met tyd. B E 30-3 Faraday s law of Induction Magnitude of magnetic field does not matter - induced emf determine by rate of change in magnetic flux. = E da = B da = BA ( B A, B In Ch 24 - Flux Amount of B through loop uniform) SI eenheid 1 weber = 1Wb = 1 Tÿm 2 SI Unit Faraday s law: Magnitude of emf E induced in conducting loop is equal to the rate at which the magnetic flux Φ B through the loop changes with time. 5

6 In volgende afdeling sal ons sien dat In next section we will see that Vir n spoel met N windings E E = = dφ B dt N dφ dt B For a coil of N turns 6

7 Voorbeeld 1 Example 1 Die magneetveld in n gebied is univorm. Dit varieer met tyd soos in figuur. Plot die stroom deur n lus wat n area van 14 cm 2 het, n weerstand van 0.02 Ω en waarvan die vlak loodreg op die magneetveld is. The magnetic field in a region is uniform. It varies with time as in Figure. Plot the current through a ring that has an area of 14 cm 2, a resistance of 0.02 Ω, and whose plane is perpendicular to the magnetic field.

8 30-4 Lenz se Wet Lenz se Wet: Die geïnduseerde stroom sal in so n rigting verskyn dat die magneetveld a.g.v. hierdie stroom die magneetveld verandering wat die stroom induseer teenwerk Rigting van geinduseerde emk Ø rigting van geinduseerde stroom Weerstand teen pool beweging: 30-4 Lenz s Law Lenz s Law: The induced current will appear in such a direction that the magnetic field due to this current opposes the change that produced it. Direction of induced emf Ø direction of induced current Opposition to pole movement: 8

9 Weerstand teen vloed verandering: Opposition to flux change: 9

10 Voorbeeld 2 Example 2 Die figuur wys n geleidende lus wat bestaan uit n halfsirkel met radius r = 0.20 m en drie reguit gedeeltes. Die halfsirkel is in n uniforme magneetveld gerig uit die bord uit; waarvan die grootte van die veld verander met die vergelyking wat gegee word; met B gemeet in tesla en t in sekondes. n Ideale battery met emk van 2.0 V is verbind aan die lus met die weerstand se waarde as 2.0 W. (a) Wat is the grootte en rigting van die geinduseerde emk rondom die lus by t = 10 s? (b) Wat is die stroom deur die lus by tydstip t = 10 s? The figure shows a conducting loop consisting of a half-cricle of radius r = 0.20 m and three straight sections. The half-circle lies in a uniform magnetic field that is directed out of the board; the field magnitude changes with time with the equation given, with B measured in teslas and t in seconds. An ideal battery with emf 2.0 V is connected to the loop. The resistance of the loop is 2.0 W. (a) What is the magnitude and direction of the induced emf around the loop at t = 10 s? (b) What is the current in the loop at t = 10 s? Φ = + 2 ( t B ) 6.0 t 7.0 t 10

11 MRI Skandeerders Magnetiese Resonansie Beelding werk met twee magneetvelde: een konstante veld, en n kleiner sinusvormige varieerende veld. Die pasient moet baie stil lê, en indien hulle nie kan nie, word hulle verdoof of n algemene narkose toegedien. Die pasient se bloedsuurstof vlak word deur n pulsoksimeter gemonitor. Die MRI prosedure behoort skadeloos te wees vir die pasient, maar as Faraday se wet nie in ag geneem word, kan die pasient brandwonde opdoen. MRI Scans Magnetic resonance imaging works using two magnetic fields: one constant field, and a smaller sinusoidally varying field. The patient must lie motionless, and if this is not possible, then the patient is sedated, usually general anaesthetic. A pulse oximeter is used to monitor the patient s blood oxygen level. The MRI procedure should be harmless, but if Faraday s Law is not taken into account, then the patient can sustain burns. 11

Department of Mathematics and Applied Mathematics Departement Wiskunde en Toegepaste Wiskunde

Department of Mathematics and Applied Mathematics Departement Wiskunde en Toegepaste Wiskunde MATHEMATICS COMPETITION WISKUNDE KOMPETISIE GRADES 0 AND GRADE 0 EN SEPTEMBER 04 SEPTEMBER 04 TIME: HOURS TYD: