PHYS.1440Lecture16 A.DanylovDepartmentofPhysicsandAppliedPhysics

Lecture 16

Chapter 29

Magnetism

Physics II

Bye, bye, Electricity.You won’t be missed.

Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-ii/

A)CapacitorA.B)CapacitorB.C)Theydischargeatthe

samerate.D)Can’tsaywithout

knowingtheinitialamountofcharge.

Whichcapacitordischargesmorequicklyaftertheswitchisclosed?

ConcepTest RC circuit 1

time constant = RC

= 12 µs = 15 µs

So the capacitor A discharges faster than B

A)5sB)4sC)2sD)1s

Whatisthetimeconstantforthedischargeofthecapacitorshowninthefigure?

ConcepTest RC circuit 3

time constant by definition = ReqC

+ =

= ReqC =4Ωx1F=4 seconds

How about this?

= ReqCeq

PHYS.1440Lecture16 A.DanylovDepartmentofPhysicsandAppliedPhysics

Today we are going to discuss:

Chapter 29:

Section 29.1-3 Section 29.5 (skip) Section 29.7

PHYS.1440Lecture16 A.DanylovDepartmentofPhysicsandAppliedPhysics

Sources of Magnetic FieldWehavelearnedthatelectricchargeqproducesanelectricfieldE

qE

Itturnsoutthatthereisanotherfield,magneticfield B,whichisproducedbyamovingelectricchargeq.

q v

(I)MovingqB B

Current

B (II)Current(manyq) B (III)Magnet B(orbitingelectrons)

B

So,therearethree systemsproducingBfield.Let’slookatthemseparately.

PHYS.1440Lecture16 A.DanylovDepartmentofPhysicsandAppliedPhysics

(III) Permanent Magnet

PHYS.1440Lecture16 A.DanylovDepartmentofPhysicsandAppliedPhysics

Magnets interact (repel/attract, observation)

The north pole of one magnet exerts anattractive force on the south pole ofanother magnet.

Like poles repel Unlike poles attract.

If the north pole of one magnet is broughtnear the north pole of another magnet,they repel each other.

PHYS.1440Lecture16 A.DanylovDepartmentofPhysicsandAppliedPhysics

There are no magnetic monopolesIf you cut a magnet in half, you don’t get a north pole and a south pole – you get two

smaller magnets.

Sheldon: “if I’m able to detect slow‐moving magneticmonopoles there, I will be the scientist to confirm string theory.People will write books about me. Third‐graders will createmacaroni‐art dioramas depicting scenes frommy life.”

Hisfriendstamperedwithhisexperimentonmagneticmonopolesbyusinganelectriccanopener.

There is no magnetic monopole

Oneofthe“BigBangTheory”episodeswasarrangedaroundthisfact.

Thereisnoexperimentalevidencethatmagneticmonopolesexist.

Anumberofattemptshavebeenmadetodetectmagneticmonopoles.SheldonCooperhasalsomadeone:

PHYS.1440Lecture16 A.DanylovDepartmentofPhysicsandAppliedPhysics

Probe object. Magnet Pole Convention

If we position a compass needle in the Earth field, one side will point to the geographical North pole.

(I) The end of a needle that points to the North geograph. pole is called the north pole (by CONVENTION).The end of a magnet that points south is called the south pole.As the result, if we follow the convention, the Earth’s “Geogr. North Pole” is a south magnetic pole, as the north end of the compass needle is attracted to it.The magnetic poles are slightly offset from the geographical poles.

*The Earth is a huge magnet due to currents in the molten iron core.

North Magnetic Pole

South Magnetic Pole

Again?

Now, we know that the magnetic field (B) exists. How can we detect B? Which object can be used as a probe system?

(0) A compass needle will be used as a probe system.

Which side of the needle should be called the North pole?Lets use the Earth’s Magnetic field*

(II) The North pole of a compass shows the direction of the magnetic field at the point.

PHYS.1440Lecture16 A.DanylovDepartmentofPhysicsandAppliedPhysics

Magnetic Fields Lines

Magneticfieldscanbevisualizedusingmagneticfieldlines,whicharealwaysclosedloops(consequenceofthefactthattherearenomagneticmonopoles).

Howtofindthesemagneticlines? With a compass needlelike a “probe charge”

B

Density of magn. lines is smaller so the magn. field is weaker

The North Pole of a compass needle shows the direction of the magnetic field

https://www.youtube.com/watch?v=8llkHQtaOlg

(II) Density of magn. lines is higher so the magnetic field is stronger

Demo:Iron filings are suspended in liquid in a clear rectangle box.

Now,sincewehaveaprobesystem,acompassneedle,wecanuseittomapamagneticfieldof,forexample,apermanentmagnet.

PHYS.1440Lecture16 A.DanylovDepartmentofPhysicsandAppliedPhysics

Vector notation and the cross (vector) product

Before we proceed with magnetic field we need to look at

PHYS.1440Lecture16 A.DanylovDepartmentofPhysicsandAppliedPhysics

Notation for Vectors and Currents Perpendicular to the Page

Magnetismrequiresathree‐dimensionalperspective,buttwo‐dimensionalfiguresareeasiertodraw.

Wewillusethefollowingnotation:

Bad karma

PHYS.1440Lecture16 A.DanylovDepartmentofPhysicsandAppliedPhysics

The Vector (Cross) Product

=(ab sinθ,directiongivenbytheright‐handrule)

Fromnowon,almostallequationswillhaveacrossproduct

Thecrossproductofvectorsa andb isavectorperpendiculartobotha andb.

[I]Pointfingersinthedirectionofthe1st (a)vector,thenbendtheminthedirectionofthe2nd one(b).Theoutstretchedthumbwillgiveadirectionofthecrossproduct

[II]Usethreefingersasshowninthefigure

Orderisimportantinthecrossproduct:

ConcepTest Cross Product

Find a direction of a cross product

PHYS.1440Lecture16 A.DanylovDepartmentofPhysicsandAppliedPhysics

Thank you