Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Maxwell's equations wikipedia , lookup
Magnetic monopole wikipedia , lookup
Field (physics) wikipedia , lookup
Magnetic field wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Electromagnetism wikipedia , lookup
Electrical resistance and conductance wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Superconductivity wikipedia , lookup
Lorentz force wikipedia , lookup
Inductors PH 203 Professor Lee Carkner Lecture 20 Ring in Solenoid If the current flows clockwise through the solenoid, the B field inside is straight down To get maximum flux, the ring should face up (parallel with the coils) We need to find the flux through the loop before and after the current is switched off F = BA cos q = BA B = m0nI = (4pX10-7)(1000)(10) = 0.0126 T A = (0.1)(0.1) = 0.01 m2 Current in Ring F = BA = (0.0126)(0.01) = 1.26 X 10-4 Wb In 1 second the flux goes to 0 DF = (1.26 X 10-4) - (0) = 1.26 X 10-4 Dt = 1 e = -N(DF/Dt) = (1)(1.26 X 10-4) = 1.26 X 10-4 V DV = iR or i = e/R = 1.26 X 10-4/10 i = 1.26 X 10-5 A Applied Induction You connect a source of motion to a magnet The changing flux produces a changing current Can easily amplify and move the current Many applications in music Microphone Electric Guitar Induction Devices Microphone Speaker Electric guitar Pickup magnet magnetizes string, the motion of which induces current Tape recorders and players The tape is magnetized such that when it passes the tape heads it induces a current How Does Induction Work? If we move the wire through a B field the electrons now have a velocity This deflection produces an imbalance of charge Finding emf e = -N(dF/dt) But the magnetic flux depends on the changing current and the properties of the coil e = -L(di/dt) where the constant of proportionality L is the inductance Inductance The unit of inductance is the henry, Equating the two expressions for e e = L(di/dt) = N(dF/dt) L = N(dF/di) Inductance is a property of the circuit element Like resistance or capacitance Solenoid Inductance To find L, we need a relationship between F and I for a solenoid Flux in general: F = BA cos q or F = BA B = m0(N/l)i or i = Bl/(m0N) L = N(dF/di) = NF/i = NBAm0N/Bl = m0N2A/l L = m0n2Al Note: N is number of turns, n is number of turns per meter Inductors In a circuit any element with a high inductance is represented by an inductor We will assume that the rest of the circuit has negligible inductance Symbol is a spiral: Motional emf If we make the loop larger or smaller, or move it in or out of a field, we will induce a potential remember emf is a potential difference (or voltage) How does motion in a field translate to voltage? Motional emf - Derived DA X L v B field into page x Consider a conductor of length L sliding on a frame with velocity v Dx in time Dt but Dx = vDt, so DA = LvDt DF/Dt = BDA/Dt = (BLvDt)/Dt e = BLv Motional emf -- Direction If the area decreases, the flux decreases and thus the induced B field is in the same direction as the original Motional emf Energy How is energy related to motional emf? The loop feels a magnetic force you have to overcome The energy goes into the electrical energy of the current in the loop P = i2R Power and Motional emf Since e = BLv and e = iR, we can write: i = BLv/R P = B2L2v2/R Large loops with low resistance moving fast in a large magnetic field will have a lot of electrical energy and thus require more work input Force on Eddy Currents Eddy Currents Imagine a loop moving out of a magnetic field As the field through the loop drops, it induces a field in the same direction If the object is not a loop, circular currents can still be induced which have the same effect Called eddy currents Metal objects moving through a magnetic field will be slowed Next Time Read 30.8-30.12 Problems: Ch 30, P: 21, 29, 31, 48, 51 What is the direction of current in the loop from the PAL (seen from top down)? A) B) C) D) E) clockwise counterclockwise left right down A ring undergoes thermal expansion while in a uniform magnetic field. If the current induced in the loop is clockwise, what is the direction of the magnetic field? A) B) C) D) E) left right into the page out of the page counterclockwise A bar magnet held north pole up is dropped straight down through a face up coil of wire. What is the direction of the current in the coil as the magnet enters and leaves the coil? A) B) C) D) E) clockwise, counterclockwise counterclockwise, clockwise clockwise, clockwise counterclockwise, counterclockwise no current is induced