Upload
others
View
8
Download
0
Embed Size (px)
Citation preview
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