Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 11

Physics 212Physics 212Lecture 17Lecture 17

BdE dl

dt

Faraday’s Law

Main Point 1

First, we introduced the concept of the magnetic flux and found that the motional emfs produced in the three examples from the last prelecture could all be written simply as the time rate of change of the magnetic flux through the circuit.

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 22

Main Point 2

Second, we introduced Faraday’s Law, which states that whenever magnetic flux changes in time, not just in the case of a moving conductor, an emf will be produced. In particular, this induced emf will just be equal to minus the time rate of change of the magnetic flux.

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 33

Main Point 3

Finally, we observed that this induced emf is determined by integrating the electric field around the loop, so that Faraday’s law can be written more generally only in terms of the electric and magnetic fields. A changing magnetic flux creates an electric field. Faraday’s law represents the first important step in establishing the deep connections between electric and magnetic fields which ultimately will explain the existence of electromagnetic waves and the identification of light as an electromagnetic phenomenon.

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 44

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 55

Bdemf E dl

dt

Faraday’s LawFaraday’s Law B B dA

Looks scary but it’s not – its amazing and beautiful ! Looks scary but it’s not – its amazing and beautiful !

A changing magnetic flux produces an electric field.A changing magnetic flux produces an electric field.

Electricity and magnetism are on intimate terms Electricity and magnetism are on intimate terms

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 66

In Practical Words:In Practical Words:

1) When the flux1) When the flux BB through a loop changes, an through a loop changes, an emfemf is induced in is induced in the loop.the loop.

There are many ways to change this…There are many ways to change this…

Faraday’s Law:Faraday’s Law:

dt

ddEemf B

wherewhere

BB

AAThink ofThink of BB as the number of field lines passing through the surfaceas the number of field lines passing through the surfaceFluxFlux Show ProjectionShow Projection

AdBB

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 77

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 88

Bdemf E dl

dt

Faraday’s LawFaraday’s Law

In Words:In Words:

1)1) When the fluxWhen the flux BB through a loop changes, an through a loop changes, an emfemf is induced in the is induced in the loop. loop. 2) The 2) The emfemf will make a current flow if it can (like a battery). will make a current flow if it can (like a battery).3) The current that flows induces a new magnetic field.3) The current that flows induces a new magnetic field.4) The new magnetic field opposes the change in the original 4) The new magnetic field opposes the change in the original magnetic field.magnetic field.

B B dA

BB

ddB/dtB/dt

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 99

The Ways Flux Can ChangeThe Ways Flux Can Change

Change Area Change magnetic field

Change orientation

ALL THESE CHANGES CAN BE UNDERSTOOD FROM MOTIONAL EMFALL THESE CHANGES CAN BE UNDERSTOOD FROM MOTIONAL EMF

WHAT’S NEW WITH FARADAY?WHAT’S NEW WITH FARADAY?

Flux can change WITHOUT moving any conductor !!Flux can change WITHOUT moving any conductor !! e.g., change current that produces magnetic field e.g., change current that produces magnetic field

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 1010

Bdemf E dl

dt

Faraday’s LawFaraday’s Law

Executive Summary:Executive Summary:

B B dA

emfemf→→current→fieldcurrent→field a) induced a) induced onlyonly when when flux is changingflux is changing b) b) opposes the changeopposes the change

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 1111

Checkpoint 1a

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 1212

A copper loop is placed in a uniform magnetic field as shown. You are looking from the right.

Suppose the loop is moving to the right. The current induced in the loop is:A. zero B. clockwise C. counterclockwise

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 1313

Checkpoint 1bCheckpoint 1b

Checkpoint 1bA copper loop is placed in a uniform magnetic field as shown. You are looking from the right.

Now suppose the that loop is stationary and that the magnetic field is decreasing in time. The current induced in the loop is: A. zero B. clockwise C. counterclockwise

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 1414

Checkpoint 1cNow suppose that the loop is spun around a vertical axis as shown, and that it makes onecomplete revolution every second.

The current induced in the loop: A. Is zeroB. Changes direction once per secondC. Changes direction twice per second

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 1515

(copper is notferromagnetic)

X O

BB

BB

Checkpoint 2A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet

Will the acceleration a of the falling ring in the presence of the magnet be any different than it would have been under the influence of just gravity (i.e. g)?A. a > g B. a = g C. a < g

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 1616

CalculationCalculation

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 1717

Conceptual Analysis

Strategic Analysis

y

xv0

aa

bb x x x x x x xx x x x x x x x x x x x x xx x x x x x xx x x x x x xx x x x x x x x x x x x x xx x x x x x x

BA rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction.

What is the direction and the magnitude of the force on the loop when half of it is in the field?

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 1818

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 1919

Physics 212 Lecture 17, Slide Physics 212 Lecture 17, Slide 2020