EM8_Manual

# EM8_Manual - General Physics II Lab EM8 Faradays law of...

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General Physics II Lab EM8 Faraday’s law of induction General Physics II Lab EM8 Faraday’s Law of Induction Purpose In this experiment, you will study Faraday’s law of induction and the mutual induction in transformers. Equipment and components Science Workshop 750 interface, magnetic field sensor, voltage sensor, bar magnet, calipers, clamp and stand, and foam (as cushion), coil of 2500 Windings, coil of 12000 Windings, U-shaped & bar soft iron core set, oscilloscope, 100 Ω resistor, BNC to 4mm plug cable, and BNC to clip cable. Background When a bar magnet passes through a coil, the changing magnetic flux through the coil induces an electromotive force (emf) across the coil. According to Faraday’s law of induction, one has d N dt φ ε =− , (1) where is the induced electromotive force (emf), N is the total number of turns of the coil, and d φ / dt is the rate of change of the magnetic flux through the coil. The negative sign in Eq. (1) indicates that the polarity of the induced emf is such that it tends to produce a current that will create a magnetic flux to oppose the change of the magnetic flux through the coil (Lenz’s law). From Eq. (1) one finds that the area under the “emf vs. time” curve represents the total magnetic flux, because dt Nd N ∫∫ . (2) Equation (1) can also be applied to a different situation, in which two coils are placed side by side. In this case, a time varying current I ( t ) passing through the first coil (the primary coil) can generate a time varying magnetic field B ( t ), which gives rise to a time varying magnetic flux φ (t) = S B ( t ) to the secondary coil, where S is the cross-sectional area of the secondary coil. As a result, an emf (or voltage) will be induced across the secondary coil. This is the working principle of transformers. Assuming that the two coils are perfect solenoids and that an alternating current, I ( t ) = I 0 cos( ω t ), is used to drive the primary coil, one can readily show that the induced emf in the secondary coil has the form 20 1 0 sin( ) NSk nI t α μωω = (3) where N 2 is the total number of turns of the secondary coil, n 1 is the number of turns per unit length of the primary coil, k is the relative permeability of the material inside the primary coil, and 0 μ is the permeability of free space. In Eq. (3) we introduce a correction factor α to account for the decrease in the magnetic field strength from the primary coil to the secondary coil. The magnetic field strength 10 1 B kn I = applies only to the inside of the primary coil a the magnetic field strength in the secondary coil is assumed to be B 2 = α B 1 . Equation (3) states that the induced emf varies alternatively in time and its amplitude is proportional to the angular frequency nd 2 f ω π = , where f is the frequency in units of Hz.

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## This note was uploaded on 03/31/2011 for the course PHYS 1 taught by Professor Nianlin during the Spring '11 term at HKUST.

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EM8_Manual - General Physics II Lab EM8 Faradays law of...

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