Physics 1402: Lecture 13Today’s Agenda

• Announcements:– Lectures posted on:

www.phys.uconn.edu/~rcote/

– HW assignments, solutions etc.

• Homework #4:Homework #4:– On Masterphysics : due Friday at 8:00 AMOn Masterphysics : due Friday at 8:00 AM

– Go to masteringphysics.com

• Midterm 1: next week (Oct. 5)– Covers Ch. 21-26

Problem Solution Method:Five Steps:

1) Focus on the Problem- draw a picture – what are we asking for?

2) Describe the physics- what physics ideas are applicable- what are the relevant variables known and unknown

3) Plan the solution- what are the relevant physics equations

4) Execute the plan- solve in terms of variables- solve in terms of numbers

5) Evaluate the answer- are the dimensions and units correct?- do the numbers make sense?

MagnetismThe Magnetic Force

x x x x x x

x x x x x x

x x x x x xv

F

B

q

x x x x x x

x x x x x x

x x x x x xFv

x x x x x x

x x x x x x

x x x x x xv

F

B

q

v

F

B

q

v

F = 0

B

q

Magnetism• Magnetic effects from natural magnets have been known for a

long time. Recorded observations from the Greeks more than 2500 years ago.

• The word magnetism comes from the Greek word for a certain type of stone (lodestone) containing iron oxide found in Magnesia, a district in northern Greece – or maybe it comes from a shepherd named Magnes who got the stuff stuck to the nails in his shoes

• Properties of lodestones: could exert forces on similar stones and could impart this property (magnetize) to a piece of iron it touched.

• Small sliver of lodestone suspended with a string will always align itself in a north-south direction. ie can detect the magnetic field produced by the earth itself. This is a compass.

Bar Magnet• Bar magnet ... two poles: N and S

Like poles repel; Unlike poles attract.

• Magnetic Field lines: (defined in same way as electric field lines, direction and density)

• Does this remind you of a similar case in electrostatics?

NS

You can see this field by bringing a magnet near a sheet covered

with iron filings

NSMagnetic Field Lines

of a bar magnet

Electric Field Linesof an Electric Dipole

Magnetic Monopoles• One explanation: there exists magnetic charge, just like

electric charge. An entity which carried this magnetic charge would be called a magnetic monopole (having + or - magnetic charge).

• How can you isolate this magnetic charge?

Try cutting a bar magnet in half:

NS N NS S

• In fact no attempt yet has been successful in finding magnetic monopoles in nature.

• Many searches have been made

• The existence of a magnetic monopole could give an explanation (within framework of QM) for the quantization of electric charge (argument of P.A.M.Dirac)

Source of Magnetic Fields?• What is the source of magnetic fields, if not magnetic

charge?

• Answer: electric charge in motion!

– eg current in wire surrounding cylinder (solenoid) produces very similar field to that of bar magnet.

• Therefore, understanding source of field generated by bar magnet lies in understanding currents at atomic level within bulk matter.

Orbits of electrons about nuclei

Intrinsic “spin” of electrons (more important effect)

Forces due to Magnetic Fields?

• Electrically charged particles come under various sorts of forces.

• As we have already seen, an electric field provides a force to a charged particle, F = qE.

• Magnets exert forces on other magnets.

• Also, a magnetic field provides a force to a charged particle, but this force is in a direction perpendicular to the direction of the magnetic field.

Definition of Magnetic FieldMagnetic field B is defined operationally by the magnetic force on a test charge.

(We did this to talk about the electric field too)

• What is "magnetic force"? How is it distinguished from "electric" force?

q

F

v

mag

Start with some observations: CRT deflection

• Empirical facts: a) magnitude: to velocity of q

b) direction: to direction of q

Lorentz Force• The force F on a charge q moving with velocity v

through a region of space with electric field E and magnetic field B is given by:

F

x x x x x x

x x x x x x

x x x x x xv

B

q

v

B

qF = 0

v

B

qF

1Units: 1 T (tesla) = 1 N / Am

1G (gauss) = 10-4 T

Lecture 13, ACT 1• Two protons each move at speed v (as shown in the

diagram) toward a region of space which contains a constant B field in the -y-direction.

– What is the relation between the magnitudes of the forces on the two protons?

(a) F1 < F2 (b) F1 = F2 (c) F1 > F2

2AB

x

y

z

1

2

v

v

Lecture 13, ACT 1• Two protons each move at speed v (as shown in the

diagram) toward a region of space which contains a constant B field in the -y-direction.

– What is the relation between the magnitudes of the forces on the two protons?

(a) F1 < F2 (b) F1 = F2 (c) F1 > F2

2AB

x

y

z

1

2

v

v

B

x

y

z

1

2

v

v

Lecture 13, ACT 1• Two protons each move at speed v (as

shown in the diagram) toward a region of space which contains a constant B field in the -y-direction.

1B

(a) F2x < 0 (b) F2x = 0 (c) F2x > 0

– What is F2x, the x-component of the force on the second proton?

F1

F2

X

X

Lecture 13, ACT 2• Cosmic rays (atomic nuclei stripped bare of

their electrons) would continuously bombard Earth’s surface if most of them were not deflected by Earth’s magnetic field. Given that Earth is, to an excellent approximation, a magnetic dipole, the intensity of cosmic rays bombarding its surface is greatest at the (The rays approach the earth radially from all directions).

A) Poles B) Equator C) Mid-lattitudes

Magnetic Force on a Current

• Consider a current-carrying wire in the presence of a magnetic field B.

• There will be a force on each of the charges moving in the wire. What will be the total force dF on a length dl of the wire?

• Suppose current is made up of n charges/volume each carrying charge q and moving with velocity v through a wire of cross-section A.

• Total force =

• Current =

N S

Simpler: For a straight length of wire L carrying a current I, the force on it is:

• Force on each charge =