PHY2049: Chapter 28 2
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
PHY2049: Chapter 28 3
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
PHY2049: Chapter 28 4
Bar MagnetsTwo poles: “north” and “south”
Like poles repel
Unlike poles attract
Magnetic poles cannot be isolated
PHY2049: Chapter 28 5
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!
PHY2049: Chapter 28 8
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!!
PHY2049: Chapter 28 9
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)
PHY2049: Chapter 28 10
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)
PHY2049: Chapter 28 11
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
PHY2049: Chapter 28 12
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
PHY2049: Chapter 28 13
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
PHY2049: Chapter 28 14
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
PHY2049: Chapter 28 15
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
PHY2049: Chapter 28 16
Right Hand RuleFirst point fingers in direction of velocity
Curl fingers toward B field⇒ Thumb points toward force
F
v
B
PHY2049: Chapter 28 17
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)
PHY2049: Chapter 28 18
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
PHY2049: Chapter 28 19
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
PHY2049: Chapter 28 20
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
PHY2049: Chapter 28 21
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=
PHY2049: Chapter 28 22
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=
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