Chapter 28: Magnetic · PDF filePHY2049: Chapter 28 2 Magnetic Fields ÎMagnetic field (units, field lines) Magnetic field of the earth and other astronomical objects ÎEffects of

PHY2049: Chapter 28 1

Chapter 28: Magnetic Fields


Magnetic Fields Magnetic field (units, field lines)

Magnetic field of the earth and other astronomical objects

Effects of magnetic fields on charges and currentsForce on a moving chargeForce on a currentTorque on a current loopPath followed by particle in magnetic field

InstrumentsMass spectrometersCyclotrons and synchrotrons


Reading QuizWhen I cut a magnet into two pieces I get:

An isolated north and south magnetic poleTwo smaller magnetsThe two pieces are no longer magnets


Bar MagnetsTwo poles: “north” and “south”

Like poles repel

Unlike poles attract

Magnetic poles cannot be isolated


Magnetic Monopoles?Can any isolated magnetic charge exist?

We would call this a “magnetic monopole”It would have a + or – magnetic charge

How can we isolate this magnetic charge?Cut a bar magnet in half? NO!

No one has ever found magnetic monopoles in natureListen to Magnetic Monopoles Song: http://www.haverford.edu/physics-astro/songs/monopoles.htm

What you getis a bunch oflittle magnets!



Bar Magnets (2)

NS

Similar to dipole field from electrostatics


Earth is a big magnet!!

Earth’s magnetic poles have reversed very frequently on a geological time scale:http://science.nasa.gov/headlines/y2003/29dec_magneticfield.htm

The North pole of a small magnet (compass) points towards geographic North because Earth’s magnetic South pole is presently up there!!


What Causes Magnetism?What is the origin of magnetic fields?

Electric charge in motion!For example, a current in a wire loop produces a field very similar to that of a bar magnet (as we shall see in Chapter 29).

Understanding the source of bar magnet field lies in understanding currents at the atomic level within matter

(More on this in Chapter 32)

Orbits of electrons about nuclei

Intrinsic “spin” of electrons (more important effect)


Law of MagnetismAnalogy with Coulomb’s Law does not work

So far no one has found magnetic monopoles (=magnetic charges)Force between two small bar magnets is complicated; turns out tobe not fundamental (should be deduced from a law that governs more fundamental phenomena)

What does this last statement mean?Magnetic field produced by bar magnet is not fundamentalMagnetic force on bar magnet is not fundamental either

Two phenomena turn out to be fundamentalElectric current produces magnetic fieldMagnetic field exerts force on moving charge

The law consists of two parts, two equationsMagnetic field produced by electric current (Chapter 29)Force due to magnetic field on moving charge (Chapter 28)


Magnetic Field UnitsFrom the expression for force on a current-carrying wire:

B = Fmax / I LUnits: newtons/A⋅m ≡ tesla (SI unit)Another unit: gauss = 10-4 tesla

Some sample magnetic field strengths:Earth: B = 0.5 gauss = 0.5 x 10-4 TGalaxy: B ∼ 10-6 gauss = 10-10 TBar magnet: B ∼ 100 gauss = 10-2 TStrong electromagnet: B = 2 T (35 T in Tallahassee)Superconducting magnet: B = 5 – 10 T (20 T in Tallahassee,

also coming soon to UF)Pulsed magnet: B ∼ 100 TNeutron star: B ∼ 108 – 109 TMagnetar: B ∼ 1011 T


PulsarsRapidly Rotating Neutron Stars

Enormous Magnetic Fields

Beam off Beam on

Crab PulsarR = 10 kmM = 1.4 solar massB ≈ 108 TPeriod = 1/30 sec

Lighthouse effect


Magnetic fields on this planet — large and small

45 tesla magnet during assembly, National High Magnetic Field Laboratory, Tallahassee, FL

Requires 30 MW (300 thousand light bulbs!)

Magnetoencephalography (MEG)detects magnetic fields produced by brain activity (electric currents): ~10-12 TSensors require a 4 K temperature


Reading QuizThe magnetic force on a moving charged particle is:

(1) Perpendicular to the velocity(2) Parallel to the velocity(3) Parallel to the B field(4) Independent of the velocity(5) None of the above


Magnetic Field BPostponing until Chapter 29 the questions of how magnetic field is

produced and how its strength is varied, large number of experiments show

Choose the unit (tesla) such that

Force magnitude depends on direction of v relative to Bv is parallel to B ⇒ sinφ = 0v is perpendicular to B ⇒ sinφ = 1v is at angle 45° to B ⇒ sinφ = 0.71

Force direction is perpendicular to both B and vRight hand rule (next slide)

For given direction of v, force magnitude is proportional to v and B

sinF qv BF qvB φ= ×=

r rr

F qvB=0F =

sin 45F qvB=

B

+q

v

F (into page)

BvqFrrr

×∝m


Right Hand RuleFirst point fingers in direction of velocity

Curl fingers toward B field⇒ Thumb points toward force

F

v

B


ExampleParticle with m = 1.5 g, q = −2µC moves with velocity 2,000 m/s through a magnetic field of 2.5 T at an angle of 30° to the field.

Magnitude of force

Direction of force?Up out of the page, from RHR

Note the negative charge!

( )( )( )( )6sin 2 10 2.5 2000 0.5 0.005NF qBv φ −= = × =

B

−q

v

F (out of page)


Reading QuizConsider +q moving relative to a B field as shown

Force is parallel to vForce is parallel to BForce is into the pageForce is out of the page

B

+q


A charged particle moves in a straight line through some region of space. Can you conclude that B = 0 here?

1. Yes2. No

A B field can exist since if v || Bthere is no magnetic force

Bq v


A particle with a negative charge enters a magnetic field region. What path will it follow?

(1) A(2) B(3) C(4) D(5) E

x x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x x

Magnetic Force

AB

C

D

E

(1) RHR says it bends down (− charge)(2) But force cannot instantaneously change v(3) So the answer is D, not E


Magnetic Force on Current-Carrying WireMagnitude of force

Easy to derive from charge, number density & drift velocity of individual charge carriers

Direction of force: RHR

sinF iBL φ=


ExampleA 4 m long wire carries current of 500A in NE direction

Magnitude of force (B = 0.5 gauss = 5 × 10-5 T, pointing N)

Direction of force?Upwards, from RHR

Can adjust current in wire to balance against gravity

Calculate mass from density, length and cross-sectional area

Good exam problem!

siniBL mgφ =

( )( )( )( )5sin 500 5 10 4 0.71 0.071NF iBL φ −= = × =

m LAρ=


Magnetic Force A vertical wire carries a current in a vertical magnetic field. What is the direction of the force on the wire?

(a) left (b) right (c) zero (d) into the page(e) out of the page

I

B

I is parallel to B, sono magnetic force

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Chapter 28: Magnetic · PDF filePHY2049: Chapter 28 2 Magnetic Fields ÎMagnetic field (units, field lines) Magnetic field of the earth and other astronomical objects ÎEffects of