L22 Ch30 Ind E Inductors
Transcript of L22 Ch30 Ind E Inductors
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Lecture 22
Chapter 30
Induced Electric Field
Physics II
This fool said some nonsense that the electric field can be
produced from the magnetic field.
Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-ii/
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Applications of Faraday’s Law
(some leftovers from the previous class)
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Applications (Faraday’s Law)
How Electric guitar works?
• Presence of a permanent magnet makes the guitar wire a magnet.
• When the magnetic guitar wire vibrates, it changes the magnetic flux in the coil.
• This flux induces a current in the coil which exactly follow the vibrations of the guitar wire.
• This current is fed to the amplifier and we can hear the sound of vibration of the guitar wire.
How Microphone works?
• When a sound wave strikes the diaphragm, a coil fixed to the diaphragm vibrates over a stationary bar magnet, changing the flux in the coil and induced an emf in the coil which is then amplified and sent to speakers.
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Applications (An Alternating-Current Generator)
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Generators
A generator is a device that transforms mechanical energy into electric energy.
A generator inside a hydroelectric dam uses electromagnetic induction to convert the mechanical energy of a spinning turbine into electric energy.
Hydroelectric Power Plant Working Animation (start at 1 min)
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Induced Electric Field
Let’s reformulate Faraday’s Law in terms of Φ
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Induced Electric FieldConsider a conducting loop in an increasing uniform magnetic field.
CCW
So,accordingtoLenz’slaw,thereisaninducedcurrentinthecounterclockwisedirection.Ifthereisacurrent,theremustbesomethingthatactsonthechargecarrierstomakethemmove,(I)soweinferthattheremustbeaninducedelectricfieldtangenttotheloopatallpoints
sdEVVVf
iif
Let’s calculate ∆V or Ɛ (emf) over the closed loop:
dtdsdE m
General form
of Faraday’s law
From Eq.26.3: sdEV
Fromtheotherside,Faraday’slaw:
Combiningthemwecanget
TheconductingloopisnotnecessarytogenerateE.(Theelectricfieldarisewhetherornotcircuitsarepresent).
Thus,(II)thespaceisfilledwithaninducedelectricfield.
Thislawimpliesthatachangingmagneticfluxwillinduceaninducedelectricfield
YoucanusetheloopwasusedasaprobesystemtoconvinceourselvesthattherewastheEfield
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Two types of the electric field
Coulomb electric field : Induced electric field:Thus, now we know two types of electric field:
1) E is produced by changing B, not by charges
2) Induced el. field lines form closed loops
3) Induced E is nonconservative
1) E is produced by charges2) Coulomb el. field lines start/stop on
charges
3) Coulomb E is conservative
dtdsdE m
0 sdE
Amazing! A changing magnetic field produces an electric field!!!
BAABm
Let’s look at the special case, when A=const and θ=0. HowcanwefindadirectionoftheinducedE?
‐ Imagine a conducting loop in thespace and use Lenz’s rule to find Iinddirection and that is Eind direction.
ConcepTest Faraday’s Law
Themagneticfieldisdecreasing.Whichistheinducedelectricfield?
E. There’s no induced field in this case.
Thefieldisthesamedirectionasinducedcurrentwouldflowiftherewerealoopinthefield.CCWImagine a loop CCW
Bind behaveslikeFlorence Nightingale
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Let’s apply Faraday’s lawIn a solenoid
EB
Eternal dance
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Induced Electric Field in a Solenoid
The current through the solenoidcreates an upward pointing magneticfield.As the current is increasing, B isincreasing, so it must induce an electricfield.
So, the induced current is clockwise.The induced electric field musttherefore be clockwise around themagnetic field lines.
EB
Eternal dance
HowcanwefindadirectionoftheinducedE?
‐ Imagine a conducting loop in thesolenoid and use Lenz’s rule to find Iinddirection and that is Eind direction.
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Induced Electric Field in a Solenoid
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Lecture 23
Chapter 30
Inductors
Physics II
Again, a violent resistance of a system to an attempt
to make some changes
Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-ii/
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Today we are going to discuss:
Chapter 30:
Section 30.8
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
InductorsInductors (solenoids) store potential energy in
a form of a magnetic field.
Ugh!It’s just energy
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Inductance (definition)Consider a solenoid of N turns with current I.
The total magnetic flux is I
Φ ~
The coefficient of proportionality is called inductance, L
The SI unit of inductance is the henry, defined as:1 henry = 1 H = 1 Wb/A = 1 T m2/A
The circuit symbol for an ideal inductor is .
The solenoid’s magnetic field passes through the coils, establishing a flux.
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Let’s find solenoid inductance
Consider a solenoid of N turns with current I.
Recall (your take-home quiz)
Φ
You see, solenoid inductance depends only on its geometry
Φ Φ ∙ ∥
PHYS.1440Lecture22 A.DanylovDepartmentofPhysicsandAppliedPhysics
Thank you