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10TH CLASSES PHYSICS DAILY PLAN discover this phenomenon and the relation between magnetism and electricity. SUBJECT: INDUCED EMF AND CURRENT AIM: to understand the Lorentz force, Faraday’s Law and the Lenz’s Law. DURATION: 3 weeks REAL LIFE: PRESENTATION: THE EMF INDUCED IN A CONDUCTOR MOVING IN A UNIFORM MAGNETIC FIELD Suppose that a conducting rod AB of length L slides on a stationary -shaped conductor as shown in Fig 4.5 The rod AB moves to the right with a velocity v , so that the velocity vector is perpendicular to the magnetic field of density, B , that is directed into the page. The charge q on the conducting rod AB moves inside the magnetic field with a velocity v . The Lorentz force acts on the charges in the rod, and as a result the charges are deflected. The end A of the rod is charged positively and the end B of the rod is charged negatively according to the right hand rule. Thus a potential difference is established between the end of A and B of the rod. The maximum potential difference between the ends A and B of the rod is the induced EMF. The Lorentz force does a work on the charges on the rod, and the work done per unit charge equals the induced emf. The induction in the rod enables us to consider the conductor moving in a magnetic field as a source of electromotive force Fig 4.1 Faraday’s experiment for electromagnetic induction From Faraday’s experiment we can get the following conclusion: When the magnetic flux in an electric circuit changes an induced electromotive force and consequently an induced electric current is produced in the circuit. The direction of the induced emf and the induced current when the flux increases are opposite to directions of the emf and the current when the flux decreases. The value of the EMF induced in the circuit shown in Figure 4.5 can be expressed in a more general form.As the conducting rod moves towards right with a speed v, each second it sweeps out an area given by the following equation: L. A t The Value of the Induced EMF can be calculated as it follows: The charge moves from A to B in a direction perpendicular to Since In 1831 faraday and Henry experimentally showed that the emf induced in a conductor was directly proportional to work done is given with the following equation: Work = Force x Displacement Work = Fmagnetic x Length of the rod Since the rod moves perpendicularly on the flux =90o the average time rate of the change in magnetic flux, ( the magnetic flux density B and it travels a distance L. The Induced emf = Work Emf in Charge t ). Since the product L. in equation 4.2 equals the area swept by F .L q q..B.L Emf .B.L in q When the rod is moved with a velocity such that it makes an angle with the lines of flux of density B, the emf induced becomes: Emfin= B.L.. Sin Emf in INDUCED ELECTROMOTIVE FORCE AND INDUCED CURRENT The discovery of electromagnetic induction that will be discussed in this chapter produces a large-scale electric current, and produces a suitable way for transportation of electric current to a far distance. Michael Faraday was able to A the conducting rod in a unit time, ( t following relation Since the changing in magnetic flux average time rate of change of the flux t = B ), we can write the BA the A t = B.L. Since the above mentioned equation equals the EMFinduced EMFinduced = - t Eq4.4 for each turn The above-mentioned equation is known as Faraday’s Law of electromagnetic induction, and it is valid for all electric circuits through which the magnetic flux changes. The minus (-) sign in this equation indicates that the direction of the induced emf is opposite to the change in magnetic flux that induces it (as it is obvious in Lenz’s Law and in law of conservation of energy). The value of the emf induced in a loop of wire containing N turns, on the other hand, is N times grater than the emf produced in a single loop. Hence: Emfin = N t Eq4.6 Example: The magnetic flux density inside a coil contains 100 turns each with a cross-sectional area 10cm2 decreases at a rate of 0.1T/sec. What is the emf induced in the coil? Solution : A= 10cm2 = 10.10-4 m2 = 10-3 m2 N= 100 B t 0.1 T / s Emfin = N t NA B t 100.10 3 .( 0.1) Emfin = 0.01 V DIRECTION OF INDUCED EMF-LENZ’S LAW Faraday’s experiment showed that work must be done to produce an induced current. Lenz was the firs to prove this fact. He has determined the direction of the induced emf as it follows: The induced current in a closed circuit produces a magnetic field that opposes the change in the external magnetic field that produces it. Lenz’s law can be applied to the case described in Fig 4.7. When the magnet is moved towards a conducting coil the magnetic flux density of the external magnetic field inside the coil increases. That is the number of the field lines linking through the coil increases (Fig 4.7a). According to Faraday’s law a current is induced in the circuit. The direction of the induced magnetic field produced by the induced current is opposite to that of the external magnetic field. Thus it tries to reduce the increasing external magnetic field. When the magnet is moved away from the coil (Fig 4.7b) the magnetic flux density of the external magnetic field inside the coil decreases. In this case the direction of the induced magnetic field produced by the induced current is the same as that of the external magnetic field. Thus it tries to strengthen the decreasing external magnetic field. Fig 4.7 a/b/c: Direction of induced current and induced magnetic field (explanation of Lenz’s law) Experiment (Lenz’s Law) An aluminum ring is slipped into the protruding iron core of a coil of 500 turns. When an AC of 220V and 50Hz is passed through the coil (Fig 4.8), the ring is thrown quite violently toward upwards and floats in the mid-air due to the repulsion force between magnetic field produced by the current induced in the ring and the field produced by the current flowing through the coil. Therefore, the ring is always repelled and floats in the air. However the effect cannot be produced if the ring has a slot in it. HOMEWORK: 43-44-45-46-47-48-49-52 MULTIMEDIA:Serway3-AkademediaElectromagnetism DEMONSTRATION: Lenz’s Law EXPERIMENT: TEACHER: DIRECTOR: