Transcript Part 1
Chapter 21 Electromagnetic Induction and Faraday’s Law Units of Chapter 21 • Induced EMF • Faraday’s Law of Induction; Lenz’s Law • EMF Induced in a Moving Conductor • Changing Magnetic Flux Produces an Electric Field • Electric Generators • Back EMF and Counter Torque; Eddy Currents • Transformers and Transmission of Power Units of Chapter 21 • Applications of Induction: Sound Systems, Computer Memory, Seismograph, GFCI • Inductance • Energy Stored in a Magnetic Field • LR Circuit • AC Circuits and Reactance • LRC Series AC Circuit • Resonance in AC Circuits 21.1 Induced EMF Almost 200 years ago, Faraday looked for evidence that a magnetic field would induce an electric current with this apparatus: 21.1 Induced EMF He found no evidence when the current was steady, but did see a current induced when the switch was turned on or off. 21.1 Induced EMF Therefore, a changing magnetic field induces an emf. Faraday’s experiment used a magnetic field that was changing because the current producing it was changing; the previous graphic shows a magnetic field that is changing because the magnet is moving. 21.2 Faraday’s Law of Induction; Lenz’s Law The induced emf in a wire loop is proportional to the rate of change of magnetic flux through the loop. Magnetic flux: Unit of magnetic flux: weber, Wb. 1 Wb = 1 T·m2 (21-1) 21.2 Faraday’s Law of Induction; Lenz’s Law This drawing shows the variables in the flux equation: 21.2 Faraday’s Law of Induction; Lenz’s Law The magnetic flux is analogous to the electric flux – it is proportional to the total number of lines passing through the loop. Example 21-2 A square loop of wire 10.0 cm on a side is in a 1.25 T magnetic field B. What are the maximum and minimum values of flux that can pass through the loop? Max value : = 0 B = BAcos = (1.25 T)(0.100 m)(0.100 m)cos0 = 0.0125 Wb Min value : = 90 B = BAcos = 0 Wb 21.2 Faraday’s Law of Induction; Lenz’s Law Faraday’s law of induction: [1 loop] (21-2a) [N loops] (21-2b) 21.2 Faraday’s Law of Induction; Lenz’s Law The minus sign gives the direction of the induced emf: A current produced by an induced emf moves in a direction so that the magnetic field it produces tends to restore the changed field. 21.2 Faraday’s Law of Induction; Lenz’s Law Magnetic flux will change if the area of the loop changes: 21.2 Faraday’s Law of Induction; Lenz’s Law Magnetic flux will change if the angle between the loop and the field changes: 21.2 Faraday’s Law of Induction; Lenz’s Law Problem Solving: Lenz’s Law 1. Determine whether the magnetic flux is increasing, decreasing, or unchanged. 2. The magnetic field due to the induced current points in the opposite direction to the original field if the flux is increasing; in the same direction if it is decreasing; and is zero if the flux is not changing. 3. Use the right-hand rule to determine the direction of the current. 4. Remember that the external field and the field due to the induced current are different. Example 21-5 A square coil of wire with a side of length 5.00 cm contains 100 loops and is positioned perpendicular to a uniform 0.600 T magnetic field. It is quickly pulled from the field at constant speed to a region where B drops abruptly to zero. At t=0, the right edge of the coil is at the edge of the field. It takes 0.100 s for the whole coil to reach the field-free region. The coil’s total resistance is 100 Ω. Find (a) the rate of change in flux through the coil, and (b) the emf and current induced. (c) How much energy is dissipated in the coil? (d) What was the average force required? (a) A = length 2 = (5.00x10 -2 m) 2 = 2.50x10 -3 m2 B = BA = (0.600 T)(2.50x10 -3 m2 ) =1.50x10 -3 Wb B 0 - (1.50x10 -3 Wb) = = -1.50x10 -2 Wb/s t 0.100 s (b) = -N B = -(100)(-1.50x10 -2 Wb/s) =1.50 V t 1.50 V I= = =1.50x10 -2 A =15.0 mA R 100 Lenz' s law : current must be clockwise to produce more B into the page and oppose the decreasing flux into the page. (c) E = Pt = I 2Rt = (1.50x10 -2 A) 2 (100 )(0.100 s) = 2.25x10 -3 J W 2.25x10 -3 J (d) F = = = 0.0450 N -2 d 5.00x10 m Exercise B What is the direction of the induced current in the circular loop due to the current shown in each part? 21.3 EMF Induced in a Moving Conductor This image shows another way the magnetic flux can change: 21.3 EMF Induced in a Moving Conductor The induced current is in a direction that tends to slow the moving bar – it will take an external force to keep it moving. 21.3 EMF Induced in a Moving Conductor The induced emf has magnitude (21-3) Measurement of blood velocity from induced emf: Example 21-6 An airplane travels 1000 km/h in a region where the earth’s magnetic field is 5.0x10-5 T and is nearly vertical. What is the potential difference induced between the wing tips that are 70 m apart? v = 1000 km/h = 280 m/s = Blv = (5.0x10 -5 T)(70 m)(280 m/s) = 1.0 V Example 21-7 The rate of blood flow in our body’s vessels can be measured using the apparatus shown below since blood contains charged ions. Suppose that the blood vessel is 2.0 mm in diameter, the magnetic field is 0.080 T, and the measured emf is 0.10 mV. What is the flow of velocity of the blood? = Blv v = Bl (1.0x10 -4 V) v= = 0.63 m/s -3 (0.080 T)(2.0x10 m) 21.4 Changing Magnetic Flux Produces an Electric Field A changing magnetic flux induces an electric field; this is a generalization of Faraday’s law. The electric field will exist regardless of whether there are any conductors around. 21.5 Electric Generators A generator is the opposite of a motor – it transforms mechanical energy into electrical energy. This is an ac generator: The axle is rotated by an external force such as falling water or steam, inducing an emf in the rotating coil. The brushes are in constant electrical contact with the slip rings. 21.5 Electric Generators A dc generator is similar, except that it has a split-ring commutator instead of slip rings.