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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/


Applications of Faraday’s Law

(some leftovers from the previous class)


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.


Applications (An Alternating-Current Generator)


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)


Induced Electric Field

Let’s reformulate Faraday’s Law in terms of Φ


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


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


Let’s apply Faraday’s lawIn a solenoid

EB

Eternal dance


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.


Induced Electric Field in a Solenoid


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/


Today we are going to discuss:

Chapter 30:

Section 30.8


InductorsInductors (solenoids) store potential energy in

a form of a magnetic field.

Ugh!It’s just energy


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.


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 ∙ ∥


Thank you