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 = BA cos = BA B = 0 nI = (4 X10 -7 )(1000)(10) = T A = (0.1)(0.1) = 0.01 m 2
Current in Ring = BA = (0.0126)(0.01) = 1.26 X Wb In 1 second the flux goes to 0 = (1.26 X ) - (0) = 1.26 X t = 1 = -N( / t) = (1)(1.26 X ) = 1.26 X V V = iR or i = /R = 1.26 X /10 i = 1.26 X 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 = -N(d /dt) But the magnetic flux depends on the changing current and the properties of the coil = -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 = L(di/dt) = N(d /dt) L = N(d /di) Inductance is a property of the circuit element Like resistance or capacitance
Solenoid Inductance To find L, we need a relationship between and I for a solenoid Flux in general: = BA cos or = BA B = 0 (N/l)i or i = Bl/( 0 N) L = N(d /di) = N /i = NBA 0 N/Bl = 0 N 2 A/l L = 0 n 2 Al 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 Consider a conductor of length L sliding on a frame with velocity v but x = v t, so A = Lv t / t = B A/ t = (BLv t)/ t = BLv X B field into page v x L x in time t AA
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 = i 2 R
Power and Motional emf Since = BLv and = iR, we can write: i = BLv/R P = B 2 L 2 v 2 /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 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)clockwise B)counterclockwise C)left D)right E)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)left B)right C)into the page D)out of the page E)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)clockwise, counterclockwise B)counterclockwise, clockwise C)clockwise, clockwise D)counterclockwise, counterclockwise E)no current is induced