Faraday's Law of Electromagnetic Induction and Lenz's Law, Schemes and Mind Maps of Law

Download Faraday's Law of Electromagnetic Induction and Lenz's Law and more Schemes and Mind Maps Law in PDF only on Docsity! Chapter 22 Electromagnetic Induction 22.4 Faraday’s Law of Electromagnetic Induction FARADAY’S LAW OF ELECTROMAGNETIC INDUCTION The average emf induced in a coil of N loops is t N tt N o o Δ ΔΦ −=$$ % & '' ( ) − Φ−Φ −=E SI Unit of Induced Emf: volt (V) the minus sign reminds us that the induced emf will oppose the change in Φ è LENZ’S LAW E Faraday’s law states that an emf is generated if the magnetic flux changes for any reason. Since Φ = BA cos φ, any change of B, A, or φ will induce an emf. (The motional emf-Φ relation we derived is a special case of this.) where, Φ = BA cos φ 22.5 Lenz’s Law Conceptual Example 8 The Emf Produced by a Moving Magnet A permanent magnet is approaching a loop of wire. The external circuit consists of a resistance. Find the direction of the induced current and the polarity of the induced emf. Since the applied magnetic field in the loop is increasing and pointing to the right, Lenz’s law says an induced current will be created in the loop to try to oppose this change by creating an induced magnetic field to the left. 22.5 Lenz’s Law Conceptual Example 9 The Emf Produced by a Moving Copper Ring. There is a constant horizontal magnetic field directed into the page in the shaded region. The field is zero outside the shaded region. A copper ring is dropped vertically through the region. For each of the five positions, determine whether an induced current exists and, if so, find its direction. Is the acceleration of the ring the same as it drops through the five positions? 22.6 Applications of Electromagnetic Induction to the Reproduction of Sound When the string of an electric guitar vibrates, an emf is induced in the coil of the pickup from the vibration of the induced magnetization in the string. The two ends of the coil are connected to the input of an amplifier which is connected to speakers. Electric guitar pickup Electric generators A battery converts chemical energy into electrical energy to produce currents and voltages in circuits. An electric generator uses Faraday’s Law to convert mechanical energy into electrical energy. è  Most of the electric power in the world is produced by electric generators! (e.g. the 120 V out of your electrical outlet) 22.7 The Electric Generator HOW AN ELECTRIC GENERATOR PRODUCES AN EMF An electric generator has essentially the same configuration as an electric motor, it is just used differently, i.e., motor: I è mechanical energy generator: mechanical energy è I 22.7 The Electric Generator Derivation of the emf induced in a rotating planar coil Use our motional emf equation for a straight wire è E = vBL where v, B, and L are all perpendicular to each other If the left vertical side of the spinning coil moves at velocity v, the component of v perpendicular to B is v sin θ , so its contribution to the emf is BLv sin θ . Since the right vertical side contributes the same emf è E = 2BLv sin θ θ is the angle between B and the normal to the plane of the loop. Example. A generator with a circular coil of 75 turns of area 3.0 x 10-2 m2 is immersed in a 0.20 T magnetic field and rotated with a frequency of 60 Hz. Find the maximum emf which is produced during a cycle. Solution: The maximum emf for a generator is E0 = NABω We know N = 75, A = 3.0 x 10-2 m2, B = 0.20 T and f = 60 Hz . Since ω = 2πf = 2π(60) = 377 radians/s E0 = (75)(3.0 x 10-2)(0.20)(377) = 170 V 22.7 The Electric Generator THE ELECTRICAL ENERGY DELIVERED BY A GENERATOR AND THE COUNTERTORQUE When the generator is delivering current, there is a an induced magnetic force acting on its coils that causes the turbine to do work so that mechanical energy is converted into electrical energy, in keeping with conservation of energy. 22.7 The Electric Generator The magnetic force gives rise to a countertorque that opposes the rotational motion. The generator has an induced motor-like action to oppose the turbine which is trying to turn it. The induced forces acting on the loop cause the countertorque. The interaction of the induced current with the applied magnetic field produces these forces.