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Induction Consider a conductor moving in a magnetic field…. X X X X X X X X X X X X X X X X X X X X The conductor is filled with mobile charges (by definition). Each charge is a moving charge in a magnetic field, and will therefore have a force exerted on it. (RHR#3) X X X X X This causes, (induces) a current to flow. X X X X X X X X X X X X + + X + X + X The conductor is filled with mobile charges (by definition). We call this X X X phenomena Electromagnetic Induction X X X X X X X X X X X X X + X + X + X + X An electromotive force (emf) is produced in a conductor whenever it cuts across magnetic field lines. No emf arises from motion parallel to a magnetic field. Coil moves Up Coil moves Down Magnetic Field Lines Calculating EMF EMF = BLvsinq EMF = Electromotive Force (Volts) B = Magnetic Field (T) L = Length of the wire (m) v = velocity of wire that is moving in the field (m/s) q = angle between wire and magnetic field Lenz’s Law: The direction of an induced current is always such that its own magnetic field opposes the magnetic field responsible for producing it. Lenz’s law is a statement of the Law of Conservation of Energy Drop a magnet through a conducting ring. S A current will be induced in the ring. N Consider a charge Q in the ring Drop a magnetic through a conducting ring. The secondary magnetic lines of force always oppose the creating lines of force. S N As the loop is pulled out of the field, a current will be induced in the loop. N pull S Induced force opposes original force Consider the force on this leg of the loop N pull S Alternating Current (AC) • Usually it isn’t a single straight wire that is moving in a external magnetic field. • Usually it is a coil of wires (like what you saw with the motor) that are rotating in the magnetic field. Remember, a coil is just a solenoid with one loop & a solenoid creates a magnetic field just like a magnet B B B B B D R A W T H I S Alternating Current (AC) • This is how the electric company generates the electricity we use. • Mechanical energy (spinning the coil) turns into electrical energy (EMF) • The catch is figuring out what will spin the coil in the external magnetic field. Effective Current & Effective Voltage 2 I eff = I max = 0.707I max 2 Veff = Units: Amps Ieff = effective current (average current) Imax = maximum current Units: Volts 2 Vmax = 0.707Vmax Veff = effective voltage (average voltage) 2 Vmax = maximum voltage In the USA, Veff = 120 V Example: A generator is created by moving a 0.20 m long wire in an external magnetic field of 2.0 T at a speed of 15 m/s. (A) What EMF is produced by the generator? EMF = BLvsinq EMF = (2.0 T)(0.20 m)(15 m/s)sin90o EMF = 6.0 V (B) If the 6.0V is the maximum voltage produced by the generator, what is the effective emf? 2 Veff = Vmax = 0.707Vmax 2 Veff = 0.707 (6.0 V) Veff = 4.2 V (C) If the generator is hooked up to a light bulb with a resistance of 2.5 W, what is the effective power of the the bulb? Remember: P = IV = I2R = V2/R Peff = (Veff)2/R Peff = (4.2)2/2.5 Peff = 7.1 W Mutual Inductance • Mutual inductance is a measure of the ability of one circuit carrying a changing current to induce an emf in a nearby circuit. • The coil carrying the current initially is called the primary coil. • The coil in which the current is induced is called the secondary coil. Transformers • Transformers are devices that change one AC potential difference to a different AC potential difference. • Real transformers are not perfectly efficient. – Efficiencies of real transformers typically range from 90% to 99%. • For this class, we will assume 100% efficiency. (We like living in an ideal world) :) Residential Power Poles usually have 3 levels of wires. High Voltage 120 –240 Volts Telephone-Cable TV Transformer There are two types of transformers: 1. Step up and 2. Step down Step up vs Step down: Think of a staircase • Step up: Start with a low voltage, end with a higher voltage • Step down: Start with a high voltage, end with a lower one. Vs Vp Vp Vs Transformers primary volts secondary volts # primary coils # secondary coils Volts x amps = Volts x amps in out Transformer Equation Vs N s Vp N p Where V = potential difference (voltage) N = # of turns in coil Subscript p refers to primary coil Subscript s refers to secondary coil Example: A step up transformer is used on a 120 V line to provide a potential difference of 2400 V. If the primary has 75 turns, how many turns must the secondary have? Vs N s Vp = 120 V Vp N p Vs = 2400 V 2400 N s 120 75 Ns = 1500 turns Np = 75 turns Ns = ? Power for a transformer • The power into a transformer equal the power out of a transformer Pp = Ps P = IV I pVp = I sVs Vs N s I p Vs I p Vp N p I s Vp I s