Faraday's Law of Induction: Induced EMF and Currents, Study notes of Physics

Download Faraday's Law of Induction: Induced EMF and Currents and more Study notes Physics in PDF only on Docsity! Induced Fields Magnetic fields may vary in time. Experiments conducted in 1831 showed that an emf can be induced in a circuit by a changing magnetic field. ▪ Experiments were done by Michael Faraday and Joseph Henry. The results of these experiments led to Faraday’s Law of Induction. An induced current is produced by a changing magnetic field. There is an induced emf associated with the induced current. A current can be produced without a battery present in the circuit. Faraday’s law of induction describes the induced emf. Introduction Michael Faraday 1791 – 1867 British physicist and chemist Great experimental scientist Contributions to early electricity include: ▪ Invention of motor, generator, and transformer ▪ Electromagnetic induction ▪ Laws of electrolysis Introduction EMF Produced by a Changing Magnetic Field, 3 The magnet is moved away from the loop. The ammeter deflects in the opposite direction. Section 31.1 Induced Current Experiment, Summary When a magnet is moved toward a loop of wire connected to a sensitive ammeter, the ammeter shows that a current is induced in the loop. When the magnet is held stationary, there is no induced current in the loop, even when the magnet is inside the loop. Section 31.1 When the magnet is moved away from the loop, the ammeter shows that the induced current is opposite that shown in part Ej. EMF Produced by a Changing Magnetic Field, Summary The ammeter deflects when the magnet is moving toward or away from the loop. The ammeter also deflects when the loop is moved toward or away from the magnet. Therefore, the loop detects that the magnet is moving relative to it. ▪ We relate this detection to a change in the magnetic field. ▪ This is the induced current that is produced by an induced emf. Section 31.1 Faraday’s Experiment – Findings At the instant the switch is closed, the ammeter changes from zero in one direction and then returns to zero. When the switch is opened, the ammeter changes in the opposite direction and then returns to zero. The ammeter reads zero when there is a steady current or when there is no current in the primary circuit. Section 31.1 Faraday’s Experiment – Conclusions An electric current can be induced in a loop by a changing magnetic field. ▪ This would be the current in the secondary circuit of this experimental set-up. The induced current exists only while the magnetic field through the loop is changing. This is generally expressed as: an induced emf is produced in the loop by the changing magnetic field. ▪ The actual existence of the magnetic flux is not sufficient to produce the induced emf, the flux must be changing. Section 31.1 Faraday’s Law of Induction – Statements The emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit. Mathematically, Remember FB is the magnetic flux through the circuit and is found by If the circuit consists of N loops, all of the same area, and if FB is the flux through one loop, an emf is induced in every loop and Faraday’s law becomes Bd ε dt F = − B dF = B A Bd ε N dt F = − Applications of Faraday’s Law – GFCI A GFCI (ground fault circuit interrupter) protects users of electrical appliances against electric shock. When the currents in the wires are in opposite directions, the flux is zero. When the return current in wire 2 changes, the flux is no longer zero. The resulting induced emf can be used to trigger a circuit breaker. Section 31.1 Applications of Faraday’s Law – Pickup Coil The pickup coil of an electric guitar uses Faraday’s law. The coil is placed near the vibrating string and causes a portion of the string to become magnetized. When the string vibrates at some frequency, the magnetized segment produces a changing flux through the coil. The induced emf is fed to an amplifier. Section 31.1 Motional emf A motional emf is the emf induced in a conductor moving through a constant magnetic field. The electrons in the conductor experience a force, that is directed along ℓ .q= F v B Section 31.2 Moving Conductor, Variations Use the active figure to adjust the applied force, the electric field and the resistance. Observe the effects on the motion of the bar. Section 31.2 Sliding Conducting Bar, cont. The induced emf is Since the resistance in the circuit is R, the current is Bd dx ε B B v dt dt F = − = − = − I ε B v R R = = Section 31.2 Sliding Conducting Bar, Energy Considerations The applied force does work on the conducting bar. ▪ Model the circuit as a nonisolated system. This moves the charges through a magnetic field and establishes a current. The change in energy of the system during some time interval must be equal to the transfer of energy into the system by work. The power input is equal to the rate at which energy is delivered to the resistor. ( ) 2 app ε P F v B v R = = =I Section 31.2 Induced Current Directions – Example A magnet is placed near a metal loop. a) Find the direction of the induced current in the loop when the magnet is pushed toward the loop (a and b). b) Find the direction of the induced current in the loop when the magnet is pulled away from the loop (c and d). Section 31.3 Induced emf and Electric Fields An electric field is created in the conductor as a result of the changing magnetic flux. Even in the absence of a conducting loop, a changing magnetic field will generate an electric field in empty space. This induced electric field is nonconservative. ▪ Unlike the electric field produced by stationary charges The emf for any closed path can be expressed as the line integral of over the path. Faraday’s law can be written in a general form: dE s Bd d dt F = −E s Section 31.4 Induced emf and Electric Fields, cont. The induced electric field is a nonconservative field that is generated by a changing magnetic field. The field cannot be an electrostatic field because if the field were electrostatic, and hence conservative, the line integral of over a closed loop would be zero and it isn’t. dE s Section 31.4 Induced emf in a Rotating Loop The induced emf in the loop is This is sinusoidal, with emax = NABw sin Bd ε N dt NABω ωt F = − = Section 31.5 Induced emf in a Rotating Loop, cont. emax occurs when wt = 90o or 270o ▪ This occurs when the magnetic field is in the plane of the coil and the time rate of change of flux is a maximum. e = 0 when wt = 0o or 180o ▪ This occurs when the magnetic field is perpendicular to the plane of the coil and the time rate of change of flux is zero. Section 31.5 DC Generators The DC (direct current) generator has essentially the same components as the AC generator. The main difference is that the contacts to the rotating loop are made using a split ring called a commutator. Use the active figure to vary the speed of rotation and observe the effect on the emf generated. Section 31.5 Motors, cont. The current in the rotating coil is limited by the back emf. ▪ The term back emf is commonly used to indicate an emf that tends to reduce the supplied current. The induced emf explains why the power requirements for starting a motor and for running it are greater for heavy loads than for light ones. Section 31.5 Hybrid Drive Systems In an automobile with a hybrid drive system, a gasoline engine and an electric motor are combined to increase the fuel economy of the vehicle and reduce its emissions. Power to the wheels can come from either the gasoline engine or the electric motor. In normal driving, the electric motor accelerates the vehicle from rest until it is moving at a speed of about 15 mph. During the acceleration periods, the engine is not running, so gasoline is not used and there is no emission. At higher speeds, the motor and engine work together so that the engine always operates at or near its most efficient speed. The result is significantly higher gas mileage than a traditional gasoline-powered automobile. Section 31.5 Eddy Currents Circulating currents called eddy currents are induced in bulk pieces of metal moving through a magnetic field. The eddy currents are in opposite directions as the plate enters or leaves the field. Eddy currents are often undesirable because they represent a transformation of mechanical energy into internal energy. Section 31.6