Magnetism

1
Magnetism
2
Magnetic Poles

• Magnets exert force on one another
• Regions of magnetic poles produce magnetic forces
• The end that points northward is called the
  north-seeking pole and vice-versa
• Each magnet has both poles-even if you take a
  magnet and break it in two, each part will have
  both poles
• Likes poles repel opposite poles attract
• Electric charges can be isolated, magnetic poles
  cannot

3
Magnetic Fields

• The space around a magnet in which a magnetic
  force is exerted, is filled with a magnetic field
• The shape of the field is revealed by magnetic
  field lines
• Magnetic Domains The magnetic field of
  individual iron atoms is so strong that
  interactions among adjacent iron atoms cause
  large clusters of them to line up with each
  other. These clusters of aligned atoms are called
  magnetic domains
• The difference between a piece of ordinary iron
  and an iron magnet is alignment of domains
• Permanent magnets are made by simple placing
  pieces of iron or certain iron alloys in strong
  magnetic fields

4
The Nature of a Magnetic Field

• A magnetic field is produced by the motion of
  electric charge
• The magnet as a whole is stationary while the
  electrons are in constant motion
• Every spinning electron is a tiny magnet

5
The Earths Magnetic Field

• The discrepancy between the orientation of a
  compass and true north is called the magnetic
  declination
• The magnetic field of the earth is not stable

6
Oersteds Discovery

• In a public experiment, Oersted showed that
  electric current could affect the motion of a
  compass needle
• The effect decreases by distance, but is not
  affected by blockage by other materials(glass,pape
  r,water, even metal)
• The effect on a compass is a torque, proportional
  to field strength B and magnetic dipole moment m
  so that tmBsinq
• Units for field strength tesla symbolized T
• Direction of the field around the wire is in
  concentric circles rotationg according to a
  right-hand rule If the thumb of the right hand
  is in the direction of the current, the curling
  fingers show the direction of the field

7
Electric Currents and Magnetic Fields

• A moving charge produces a magnetic field, many
  of these with an electric current
• Magnetic field lines about a current-carrying
  wire crowd up when the wire is bent into a loop
• A piece of iron placed in a current-carrying coil
  of wire is an electromagnet

8
Magnetic Forces on Current-Carrying Wires

• Current-carrying wires respond to deflected
  force, moving the wire
• If the direction of the current is reversed, the
  deflected force acts in the opposite direction
• The force is maximum when the current is
  perpendicular to the magnetic field lines
• The value of this force depends on current,
  length of the wire in the field, field strength,
  and angle between direction of current and field
  F I l B sin q

9
Example 19.1

• A straight wire thru a field of 1.00 T which is
  0.250 m wide is perpendicular to the field. What
  current must be in the wire to produce a force of
  9.81 N?
• Rearrange the force equation to find current
• I F 9.81
  39.2 A
• l B sin q (.250)(1.00)(1.00)

10
Magnetic Forces on Moving Charged Particles

• A charged particle at rest will not interact with
  a static magnetic field
• A charged particle that moves in a magnetic
  field, the magnetic character of its motion
  becomes evident, experiencing a deflected force
• The force is greatest when the particle moves in
  a direction perpendicular to the magnetic field
  lines
• At other angles the force is less
• It becomes zero when the particle moves parallel
  to the field lines
• Value of this force depends on charge, velocity,
  field strength, and angle between field and
  motion
• F q v B sin q
• If a charged particle were injected into a
  magnetic field, it would follow a circular path,
  with radius controlled by mass, velocity, charge,
  and field r m v This equation is
  used in nuclear research.
• q B

11
Magnetic Field of a Current Carrying Wire

• The value of field strength at any point around a
  current carrying wire was found by Biot and
  Savart not long after Oersteds experiment
• The equation for B where k has value
• of 10-7 N/A2
• Example 19.5
• What is the magnitude of the magnetic field 3.0 m
  from a wire carrying 15 A?
• Use the equation B k 2I (10-7) (2)(15)
  1.0 10-6 T
• d 3.0

12
Force Between Two Wires

• Two current carrying wires exert forces on each
  other, depending on relative current direction
• If both currents are in same direction, the force
  is attractive if opposite, the forces are
  repulsive
• The force per unit length is easiest to measure
  and its equation, if the currents are equal, is

13
Magnetic Field in a Wire Loop

• A special case is that of a magnetic field at the
  center of a circular wire loop
• Re-defining k in terms of mo allows elimination
  of p in equations k mo / 4p
• This makes the equation for B moI
• 2r

14
Example 19.6

• What radius loop will a copper wire of resistance
  per unit length 0.068 W/m, connected to a 6.3 V
  battery, have the same field as the earth, 5.0
  10-5 T ?
• Resistance would be (R/l) x circumference(2pr)
  and IV/R so IV/ (2pr)(R/l)
• Field strength becomes B moI /2r mo V/
  (4pr2)(R/l)
• Rearranging for r
• r 0.43 m

15
Magnetic Force on a Current Loop

• If a rectangular loop in a constant field is
  considered, two sides will be parallel and two
  perpendicular to the field. Those parallel to
  the field have forces equal and opposite and thus
  no torque is created, but those perpendicular
  will have torques adding to make tIAB sin q
  where A is the area of the loop.
• The current loop becomes a magnetic dipole with
  moment mIA and direction related to another
  right-hand rule
• The direction of the magnetic moment is the
  direction of the right thumb as the fingers curl
  in the direction of the current
• Since loops can be multiplied, the moment can be
  calculated for N loops as mNIA

16
Example 19.7

• A flat coil of 25 loops has a radius of 5.5 cm.
• a. What is the magnetic moment if the current is
  1.5 A?
• b. What is the maximum torque exerted on it by
  the earths magnetic field? (B 5.0 x 10-5 T)
• a. mNIA (25)(1.5)(p(5.5x10-2)2) 0.36 A m2
• b. tmBsinq (0.36)(5.0 x 10-5)(1.0) 1.8 x 10-5
  Nm

17
Meters for Current and Voltage

• A current-indicating instrument which utilizes
  the torque from a magnetic field is the
  galvanometer
• A galvanometer may be calibrated to measure
  current in amperes to make an ammeter. Ammeters
  are usually constructed with a resistance in
  parallel to control current range.
• Ammeters calibrated to measure electric potential
  (volts) is a voltmeter. Voltmeters are
  constructed with a resistance in series to limit
  the current passing thru the meter.

18
Example 19.8

• What resistance must be used in series with a
  galvanometer of resistance 10 kW with full
  deflection at 100 mA to make a meter which will
  measure 100 V?
• The required resistance for the total meter would
  be Rv V/I 100 / (100x 10-6) 106 W
• The added series resistor would be
• R Rv -Rm 106 - 10 x 103 990,000 W

19
Homework Chapter 19

• Pp.552-554
• 6, 7, 14, 20, 34, 36, 43, 48

20
Electromagnetic Induction

• Faraday discovered that a current carrying wire
  can induce a current in a nearby wire if the
  current in the first wire is continually changing
• The amount of voltage induced depends on how
  quickly the magnetic field lines are traversed by
  the wire (the quicker the more voltage) V? rate
  of change of magnetic flux
• Formula for magnetic flux fm thru area A and
  magnetic field B is fm BA cos q
• The greater number of loops of wire that move in
  a magnetic field, the greater the induced voltage
  and the greater the current in the wire
• The voltage, or emf, in a series of N loops
  becomes
• E

21
Electromagnetic Induction

• Lenzs Law states the direction of the induced
  current in a coil is such that its own magnetic
  field opposes the original change in magnetic
  flux that induced the current.
• This means it is more difficult to push the
  magnet into a coil with more loops because the
  magnetic field of each current loop resists the
  motion of the magnet.
• The phenomena of inducing voltage by changing the
  magnetic field around a conductor is called
  electromagnetic induction.

22
Examples 20.1 20.2

• What emf is produced in a square coil of wire
  with 20 turns and 10 cm on a side which is
  removed from a field of 0.25 T in 0.10 s?
• Use fm BA cos q where since q 0º, then cos q
  1 and fm BA
• so fm (0.25)(.10)2 0.0025
• E -Nfm/t -20(0.0025) / 0.10 0.50 V
• Find the current thru a 37 W resistor connected
  to a 5 turn circular loop of diameter 10 cm with
  a field change rate of 0.050 T/s.
• I E /R (-NDfm/DtR) (-NDBA/DtR)(-NDBp(D/2)2/Dt
  R)
• I -NpD2(DB/Dt) - 5 p(0.10)2(0.050)
  -53 x 10-6 A
• 4 R 4(37)

23
Motional EMF

• If a wire moves in a constant field, the effect
  is the same as a stationary wire in a changing
  field
• E

Example 20.3 How fast must a 0.27 m aluminum rod
be moved in a 0.89 T field to generate an emf of
1.5 V? E Blv so v E/Bl 1.5 / (0.89)(0.27)
6.2 m/s
24
Generators and Alternating Current

• Generators convert mechanical energy into
  electrical by rotating a coil of wire in a
  magnetic field. This induced voltage alternates
  in direction and the frequency of the induced
  alternating voltage is equal to the frequency of
  the changing magnetic field within the loop.
• As the coil is rotated, the magnetic flux thru
  the coil continually changes. The induced emf is
  drawn off the coil by rotating contacts.
• The emf created varies in value from positive to
  negative in a sinusoidal fashion. Since q can be
  expressed as w t ,angular speed times seconds,
  then emf can be expressed likewise E w BA
  sin w t
• In a closed circuit, it produces an alternating
  current

25
Example 20.4

• A 25 loop coil of area 0.010 m2 rotated in
  earths magnetic field at a frequency of 60 Hz
  produces an emf. What is its value?
• E Nw BA at peak, where sin w t 1
• since w 2p f, this becomes E N 2p f BA
• E (25)(2p)(60)(5.0 x 10-5)(0.010) 4.7 x 10-3 V

26
Electric Motors

• If the design of the generator is reversed, you
  have an electric motor, where electric current
  causes repulsion against a magnet to produce
  motion
• Large motors are usually made with an
  electromagnet that is energized by a power source
  with many loops of wire that are wound about an
  iron cylinder, called an armature which then
  rotates when energized with electric current
• Motor and Generator Comparison Moving charges
  experience a force that is perpendicular to both
  their motion and the magnetic field that they
  traverse.
• The deflected wire is the motor effect, and the
  law of induction is the generator effect

27
Transformers

• Transformers are made from two multiturn coils of
  wire on an iron core. It allows an increase or
  decrease of AC voltage without appreciable power
  loss. The iron core allows better transfer of
  magnetic flux and better magnetic coupling than
  thru air. The relationship between the two
  circuits is shown in the formula
• primary voltage
  secondary voltage
• number of primary turns number of
  secondary turns
• V1 V2 V1 N1
• N1 N2 V2 N2
• Power into primary power out of secondary
• (voltage current)primary (voltage
  current)secondary

28
Example 20.6

• A 20 W desk lamp has resistance of 7.2 W. If the
  current to the lamp comes from a transformer with
  primary voltage of 120 V AC,
• a. What is the ratio of primary to secondary
  turns?
• b. What is the minimum current thru the primary?
• P2 V22 /R2 so V2 ? P2R2 ? (20)(7.2) 12 V
• V1/ V2 N1/ N2 120 / 12 10
• V1I1 V2I2 I2 V2 / R2 12 / 7.2 1.67 A
• (120)I1 (12)(1.67) I1 0.167 A

29
Power Transmission

• Almost all power today is AC and the voltage is
  transferred in different levels
• Power created at 6000 V then raised to 120000 V
• Power is reduced when it comes to user

30
Induction of Electric and Magnetic Fields

• An electric field is induced in any region of
  space in which a magnetic field is changing with
  time.
• The magnitude of the induced electrical field is
  proportional to the rate at which the magnetic
  field changes.
• The direction of the induced electric field is at
  right angles to the changing magnetic field
• A magnetic field is induced in any region of
  space in which an electric field is changing with
  time.
• The magnitude of the induced magnetic field is
  proportional to the rate at which the electric
  field changes.
• The direction of the induced magnetic field is at
  right angles to the changing electric field

31
Electromagnetic Waves

• Shake a charged object to and fro and you produce
  electromagnetic waves.
• An electromagnetic wave is composed of vibrating
  electric and magnetic fields that regenerate each
  other

32
Homework

• pp. 576-578
• 2, 6, 10, 15, 16, 20, 22

33
Hooo-RAH!!

• Nada--NOTHING from chapter 21 on the B test!!!!
• Scared you for nothing I guess!!

34
EQUATIONS!!
tmBsinq F I l B sin q F q v B sin q r
m v / q B B k2I/d moI/2pd mNIA tIAB sin
q mBsinq fm BA cos q E -NDfm/ D t E
Blv E w BA sin w t V1 V2
V1 N1 N1 N2 V2
N2 V1I1 V2I2