inductors ph 203 professor lee carkner lecture 20
Post on 19-Dec-2015
215 views
TRANSCRIPT
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 = 0nI = (4X10-7)(1000)(10) = 0.0126 T
A = (0.1)(0.1) = 0.01 m2
Current in Ring
= BA = (0.0126)(0.01) = 1.26 X 10-4 Wb In 1 second the flux goes to 0 = (1.26 X 10-4) - (0) = 1.26 X 10-4
t = 1 = -N(/t) = (1)(1.26 X 10-4) = 1.26 X 10-4 V V = iR or i = /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
= -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/(0N)
L = N(d/di) = N/i = NBA0N/Bl = 0N2A/l
L = 0n2Al 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 = vt, so A = Lvt
/t = BA/t = (BLvt)/t = BLv
X
B field into page
v
x
L
x in time t
A
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 = BLv and = 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) 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