Magnetism

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Magnetism

• Magnetism
• Permanent and Temporary
• 1

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Assignments

• 24/1-9,16-18,21-23, and 669/1-9
• 25/1-8,16,17,21

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General Properties of Magnets

• Like magnetic poles repel unlike magnetic poles
  attract
• Magnetic field lines are directed from north to
  south
• Magnetic field lines always form close loops
• A magnetic field exists around any wire that
  carries current

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Bar Magnets
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Genl Properties cont.

• A coil of wire (SOLENOID) that carries a current
  has a magnetic field about a permanent magnet

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Forces Caused by Magnetic Fields

• When a current-carrying wire is placed in a
  magnetic field, a force acts on the wire that is
  perpendicular to both the field and the wire.
  Meters operate on this principle.
• Magnetic field strength is measured in tesla, T
  (one newton per ampere per meter).
• B is the symbol for magnetic field

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Forces cont.

• An electric motor consists of a coil of wire
  (armature) placed in a magnetic field. When
  current flows in the coil, the coil rotates as a
  result of the force on the wire in the magnetic
  field.
• The force a magnetic field exerts on a charged
  particle depends on the velocity and charge of
  the particle and the strength

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Forces cont.

• of the magnetic field. The direction of the
  force is perpendicular to both the field and
  particles velocity.

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Key Equations

• F BIL ? Force on a current carrying wire in a
  magnetic field. Force magnetic field strength
  x current x length of wire. Newton tesla x amp
  x meter
• F BqV ? Force of a magnetic field on a single
  charged particle. Force magnetic field
  strength x charge x velocity of the charge.
  Newton tesla x coulomb x m/s

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Hand Rule 1- B field direction around a current
carrying wire

• Point thumb in direction of current in the wire
• Fingers of your hand circle the wire and show the
  direction of the magnetic field
• Knuckles, N
• Finger tips, S

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Hand Rule 2 Determine the polarity of an
electromagnet

• Wrap the fingers of your right hand around the
  loops in the direction of the current
• Extended thumb points toward the N pole of the
  electromagnet

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Sample Problems

• A straight wire that carries a 5.0 amp current is
  in a uniform magnetic field oriented at right
  angles to the wire. When 0.10 m of the wire is
  in the field, the force on the wire is 0.20 n.
  What is the strength of the magnetic field, B?

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Solution

• Known Unknown
• I 5.0 amp B ?
• L 0.10m
• F 0.20 N
• FBIL ? B F/IL
• 0.20N/5.0 amp(0.10m)
• 0.40 T

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Sample Problem

• A beam of electrons travels at 3.0 x 106 m/s
  through a uniform magnetic field of 4.0 x 101 T
  at right angles to the field. How strong is the
  force that acts on each electron?
• Known Unknown
• V 3.0 x 106 m/s F ?
• B 4.0 x 101 T
• Q - 1.6 x 1019 c

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Solution

• F BqV
• 4.0 x 101 T (-1.6 x 1019c)(3.0 x 106 m/s)
• -1.9 x 1013 Tcm/s
• -1.9 x 10 -13 n

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The small picture how magnetism occurs

• Domain theory when enough atoms of a substance
  line up in the same direction
• Strong magnets iron and steel
• Very strong Alnico alloy
• Weak aluminum, platinum
• Natural magnetite or lodestodes formed when
  rock was molten

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Magnetic field lines

• Magnetic flux, (F) number of field lines
  passing through a surface
• Unit weber 1 nm/amp
• Magnetic flux density, B F /A
• Unit wb/m2 nm/a m2 n/am
• 1 wb/m2 1 Tesla
• Earth, 104 T Humans, 1011 T

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Electromagnetism-flowing electrical current ?
magnetism

• Amperes Rule for parallel, straight conductors
  F 2k L I1 I2 / d
• K 10 7 n/a2 10 7 Tm/a
• L, length, m
• I, current, a
• d, distance between wires

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Solenoid conducting linear coil which acts like
a bar magnet

• Increase B, magnetic flux density by
• Increasing the current
• Adding loops of wire
• Inserting an iron core into solenoid now it is
  an electromagnet

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Electromagnetic Induction
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Michael Faraday and Joseph Henry around the same
time

• Discovered that when there is relative motion
  between a magnetic field and a complete circuit
  (and the conductor cuts across the magnetic
  field), that electricity will flow!!!

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Hand rule 3 shows force acting on wire in B
field

• Lay right hand flat, palm up
• Extend thumb 90 degrees to rest of fingers
• Fingers point in direction of B field
• Thumb points in direction of current, I
• Imaginary vector coming up perpendicular out of
  the palm points in the direction of force acting
  on current carrying wire.

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If current flows, there must be an EMF this is
EM induction

• Faradays Law of Induction
• E - N DF / D t
• E, emf, volts
• -N, of turns of wire (- means the current
  opposes the change that induced it)
• DF, change in flux in weber, wb
• D t, change in time, sec

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Sample Problem

• If a coil of 200 turns is moved perpendicularly
  in a magntic field at a constant rate, find the
  induced emf. The flux linkage change ( DF / D t)
  is 4.00 x 10-6 wb in 0.0100 sec.

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Problem solution

• E - N DF / D t
• E (-200)(4.00 x 10 6 wb)
• 1.00 x 10 2 s
• E -8.00 x 10 2 v
• Imagine what thousands of turns would produce!

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Generators at Hoover Dam
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Electric Generators

• Convert mechanical energy into electrical energy
  by rotating a looped conductor (armature) in a
  magnetic field
• Alternating-Current electricity produced is
  conducted by slip rings and brushes to be
  used
• Direct current can be produced by using split
  rings

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A coil with a wire is wound around a 2.0 m2
hollow tube 35 times. A uniform magnetic field is
applied perpendicular to the plane of the coil.
If the field changes uniformly from 0.00 T to
0.55 T in 0.85 s, what is the induced emf in the
coil?
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A 2.0 m2 N 35 B .55 T T 0.85 s E -N D F
/ D t - NBA / D t E 35 (0.55 T) (2 m 2)
0.85s E 45.3 v
http//www.phys.ufl.edu/phy3054/extras/contents/W
elcome.html
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AC Generator Output
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Four sides of a loop depicted in a magnetic field
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Cross-section of a rotating wire loop and output
current
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Lenzs Law -

• The direction of an induced current is such that
  the magnetic field resulting from the induced
  current opposes the change in the field that
  caused the induced current.
• When the N pole of a magnet is moved toward the
  left end of a coil, that end of the coil must
  become a N, causing induced current flow in
  opposition.

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• Lenz's law The induced emf generates a current
  that sets up a magnetic field which acts to
  oppose the change in magnetic flux.

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• Another way of stating Lenz's law is to say that
  coils and loops like to maintain the status quo
  (i.e., they don't like change). If a coil has
  zero magnetic flux, when a magnet is brought
  close then, while the flux is changing, the coil
  will set up its own magnetic field that points
  opposite to the field from the magnet.

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• On the other hand, a coil with a particular flux
  from an external magnetic field will set up its
  own magnetic field in an attempt to maintain the
  flux at a constant level if the external field
  (and therefore flux) is changed.

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Inductance

• The property of an electric circuit by which a
  varying current induces a back emf in that
  circuit or a neighboring circuit.
• Mutual Inductance, M
• Self Inductance, L

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Mutual Inductance

• Effect that occurs in a transformer when a
  varying magnetic field created in the primary
  coil is carried through the iron core to the
  secondary coil, where the varying field induces a
  varying emf.

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M -Es / D Ip/ D t

• Shows the ratio of induced emf in one circuit to
  the rate of change of current in the other
  circuit.
• M, inductance, Henry
• Es, average induced emf across secondary
• D Ip/ D t, time rate of change in current in
  primary coil
• - sign, induced v opposes D I

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Problem

• Find the mutual inductance in an electrical
  device in which the EMF in the secondary is 200.
  V and the rate of change of the current is 2.0 x
  10-3 a/s.
• M -Es / D Ip/ D t
• M -200v / 2.0x10-3a/s
• M -1x105 H

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Self Inductance

• Ratio of induced emf across a coil to the rate of
  change of current in the coil
• L -E / D I / D t
• L, henry
• I, current, amp
• T, time, sec

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Effective Value
Ieff 0.707 Imax Veff 0.707 Vmax

• www.sfu.ca/.../Graphics/Root_Mean_Square.gif

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Transformer

• Two separate coils of wire placed near one
  another that are used to increase or decrease AC
  voltages with little loss of energy.
• It contains a Primary coil and a Secondary coil
• When the primary is connected to AC voltage, the
  changing current creates a varying magnetic field
  that is carried through the core to the secondary
  coil.

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Transformer, cont.

• In the secondary coil, the varying field induces
  a varying emf. This is called mutual inductance
• Secondary voltage secondary turns
• Primary voltage primary turns
• Power Voltage x Current

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Transformers lose no power

• Pp Ps ? VpIp VsIs
• Transformer Equation
• Is Vp Np
• Ip Vs Ns

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Transformer Problem

• A step-up transformer has a primary coil
  consisting of 200 turns and a secondary coil that
  has 3000 turns. The primary coil is supplied
  with an effective AC voltage of 90.0v. A)What is
  the Vs? B)If Is 2.00a, find Ip. C) What is
  the power in the primary circuit?

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Solution to Transformer Problem

• Vs NsVp/Np 3000(90.0V)/200 1.35 kV
• Pp Ps, VpIp VsIs ? Ip VsIs/Vp
• Ip 1350v(2.00a)/90.0v 30.0a
• Pp VpIp 90.0v(30.0a) 2.70 kW

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Assignment 488p1,5,7

• 1. Ns VsNp/Vp(2400v)(75turns)/120v 1500 turns
• 5. A. Vs VpNs/Np 120v/5 24.0 v
• 5. B. Is Vs/Rs 24v/15 W 1.60 a
• 5. C. Ps(Is)2 Rs (1.60a)2 (15.0 W )
• 38.4 w

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Sources or for more information

• http//physics.bu.edu/duffy/py106.html
• http//sol.sci.uop.edu/jfalward/magneticforcesfie
  lds/magneticforcesfields.html
• Most any high school or college physics text
• www.physics.sjsu.edu/.../physics51/mag_field.htm
• hyperphysics.phy-astr.gsu.edu/.../elemag.html 52