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Chapter 19. Magnetism. Magnets have two ends – poles – called north and south. Like poles repel; unlike poles attract. If you cut a magnet in half, you don’t get a north pole and a south pole – you get two smaller magnets. Types of Magnetic Materials.

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chapter 19

Chapter 19

Magnetism

slide3

If you cut a magnet in half, you don’t get a north pole and a south pole – you get two smaller magnets.

types of magnetic materials
Types of Magnetic Materials
  • Soft magnetic materials, such as iron, are easily magnetized
    • They also tend to lose their magnetism easily
  • Hard magnetic materials, such as cobalt and nickel, are difficult to magnetize
    • They tend to retain their magnetism
sources of magnetic fields
Sources of Magnetic Fields
  • The region of space surrounding a moving charge includes a magnetic field
    • The charge will also be surrounded by an electric field
  • A magnetic field surrounds a properly magnetized magnetic material
magnetic fields
Magnetic Fields
  • A vector quantity
  • Symbolized by
  • Direction is given by the direction a north pole of a compass needle points in that location
  • Magnetic field lines can be used to show how the field lines, as traced out by a compass, would look
magnetic field lines sketch
Magnetic Field Lines, sketch
  • A compass can be used to show the direction of the magnetic field lines (a)
  • A sketch of the magnetic field lines (b)
magnetic field lines bar magnet
Magnetic Field Lines, Bar Magnet
  • Iron filings are used to show the pattern of the magnetic field lines
  • The direction of the field is the direction a north pole would point
magnetic field lines unlike poles
Magnetic Field Lines, Unlike Poles
  • Iron filings are used to show the pattern of the magnetic field lines
  • The direction of the field is the direction a north pole would point
    • Compare to the magnetic field produced by an electric dipole
magnetic field lines like poles
Magnetic Field Lines, Like Poles
  • Iron filings are used to show the pattern of the electric field lines
  • The direction of the field is the direction a north pole would point
    • Compare to the electric field produced by like charges
earth s magnetic field
Earth’s Magnetic Field
  • The Earth’s geographic north pole corresponds to a magnetic south pole
  • The Earth’s geographic south pole corresponds to a magnetic north pole
    • Strictly speaking, a north pole should be a “north-seeking” pole and a south pole a “south-seeking” pole
earth s magnetic field12
Earth’s Magnetic Field
  • The Earth’s magnetic field resembles that achieved by burying a huge bar magnet deep in the Earth’s interior
more about the earth s magnetic poles
More About the Earth’s Magnetic Poles
  • The magnetic and geographic poles are not in the same exact location
    • The difference between true north, at the geographic north pole, and magnetic north is called the magnetic declination
      • The amount of declination varies by location on the earth’s surface
source of the earth s magnetic field
Source of the Earth’s Magnetic Field
  • There cannot be large masses of permanently magnetized materials since the high temperatures of the core prevent materials from retaining permanent magnetization
  • The most likely source of the Earth’s magnetic field is believed to be electric currents in the liquid part of the core
reversals of the earth s magnetic field
Reversals of the Earth’s Magnetic Field
  • The direction of the Earth’s magnetic field reverses every few million years
    • Evidence of these reversals are found in basalts resulting from volcanic activity
    • The origin of the reversals is not understood
magnetic fields17
Magnetic Fields
  • When moving through a magnetic field, a charged particle experiences a magnetic force
    • This force has a maximum value when the charge moves perpendicularly to the magnetic field lines
    • This force is zero when the charge moves along the field lines
magnetic fields cont
Magnetic Fields, cont
  • One can define a magnetic field in terms of the magnetic force exerted on a test charge moving in the field with velocity
    • Similar to the way electric fields are defined
units of magnetic field
Units of Magnetic Field
  • The SI unit of magnetic field is the Tesla (T)
    • Wb is a Weber
  • The cgs unit is a Gauss (G)
    • 1 T = 104 G
a few typical b values
A Few Typical B Values
  • Conventional laboratory magnets
    • 25000 G or 2.5 T
  • Superconducting magnets
    • 300000 G or 30 T
  • Earth’s magnetic field
    • 0.5 G or 5 x 10-5 T
finding the direction of magnetic force
Finding the Direction of Magnetic Force
  • Experiments show that the direction of the magnetic force is always perpendicular to both and
  • Fmax occurs when is perpendicular to
  • F = 0 when is parallel to
right hand rule 1
Right Hand Rule #1
  • Place your fingers in the direction of
  • Curl the fingers in the direction of the magnetic field,
  • Your thumb points in the direction of the force, , on a positive charge
    • If the charge is negative, the force is opposite that determined by the right hand rule
slide23

x x x x x x

x x x x x x

x x x x x x

v

q

1) out of the page

2) into the page

3) downwards

4) to the right

5) to the left

A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?

slide24

A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?

x x x x x x

x x x x x x

x x x x x x

v

q

F

1) out of the page

2) into the page

3) downwards

4) to the right

5) to the left

Using the right-hand rule, you can see that the magnetic force is directed to the left. Remember that the magnetic force must be perpendicularto BOTH the B field and the velocity.

slide25

x x x x x x

x x x x x x

x x x x x x

v

q

1) out of the page

2) into the page

3) downwards

4) upwards

5) to the left

A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?

slide26

x x x x x x

x x x x x x

x x x x x x

F

v

q

A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?

1) out of the page

2) into the page

3) downwards

4) upwards

5) to the left

Using the right-hand rule, you can see that the magnetic force is directed upwards. Remember that the magnetic force must be perpendicularto BOTH the B field and the velocity.

slide27

® ® ® ® ®

® ® ® ® ®

v

® ® ® ® ®

® ® ® ® ®

q

1) out of the page

2) into the page

3) zero

4) to the right

5) to the left

A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?

slide28

® ® ® ® ®

® ® ® ® ®

v

® ® ® ® ®

® ® ® ® ®

´

q

F

A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?

1) out of the page

2) into the page

3) zero

4) to the right

5) to the left

Using the right-hand rule, you can see that the magnetic force is directed into the page. Remember that the magnetic force must be perpendicularto BOTH the B field and the velocity.

slide29

­ ­ ­ ­ ­ ­ ­ ­

­ ­ ­ ­ ­ ­ ­ ­

v

­ ­ ­ ­ ­ ­ ­ ­

­ ­ ­ ­ ­ ­ ­ ­

q

1) out of the page

2) into the page

3) zero

4) to the right

5) to the left

A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?

slide30

­ ­ ­ ­ ­ ­ ­ ­

­ ­ ­ ­ ­ ­ ­ ­

v

­ ­ ­ ­ ­ ­ ­ ­

­ ­ ­ ­ ­ ­ ­ ­

q

F = 0

A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?

1) out of the page

2) into the page

3) zero

4) to the right

5) to the left

The charge is moving parallel to the magnetic field, so it does not experience any magnetic force. Remember that the magnetic force is given by: F = v B sin(q) .

quick quiz
Quick Quiz

A charged particle moves in a straight line through a region of space. Which of the following answers must be true? (Assume any other fields are negligible.) The magnetic field (a) has a magnitude of zero (b) has a zero component perpendicular to the particle’s velocity (c) has a zero component parallel to the particle’s velocity in that region.

answer
Answer

(b). The force that a magnetic field exerts on a charged particle moving through it is given by , where is the component of the field perpendicular to the particle’s velocity. Since the particle moves in a straight line, the magnetic force (and hence , since ) must be zero.

quick quiz33
Quick Quiz

The north-pole end of a bar magnet is held near a stationary positively charged piece of plastic. Is the plastic (a) attracted, (b) repelled, or (c) unaffected by the magnet?

answer34
Answer

(c). The magnetic force exerted by a magnetic field on a charge is proportional to the charge’s velocity relative to the field. If the charge is stationary, as in this situation, there is no magnetic force.

slide35

1

x x x x x x x x x x x x

x x x x x x x x x x x x

x x x x x x x x x x x x

x x x x x x x x x x x x

x x x x x x x x x x x x

x x x x x x x x x x x x

2

3

4

A beam of atoms enters a magnetic field region. What path will the atoms follow?

slide36

1

x x x x x x x x x x x x

x x x x x x x x x x x x

x x x x x x x x x x x x

x x x x x x x x x x x x

x x x x x x x x x x x x

x x x x x x x x x x x x

2

3

4

A beam of atoms enters a magnetic field region. What path will the atoms follow?

Atoms are neutral objects whose net charge is zero. Thus they do not experience a magnetic force.

example 1
Example 1

An electron gun fires electrons into a magneticfield directed straight downward. Find the direction of theforce exerted by the field on an electron for each of the followingdirections of the electron’s velocity: (a) horizontaland due north; (b) horizontal and 30° west of north; (c) duenorth, but at 30° below the horizontal; (d) straight upward.(Remember that an electron has a negative charge.)

example 2
Example 2

(a) Find the direction of the force on a proton (a positivelycharged particle) moving through the magnetic fieldsin Figure P19.2, as shown. (b) Repeat part (a),assuming the moving particle is an electron.

example 3
Example 3

An electron is accelerated through 2 400 V from rest andthen enters a region where there is a uniform 1.70-T magneticfield. What are (a) the maximum and (b) the minimummagnitudes of the magnetic force acting on thiselectron?

practice 1
Practice 1

A proton moves perpendicularly to a uniform magneticfield at 1.0 × 107 m/s and exhibits an acceleration of2.0 × 1013 m/s2 in the +x-direction when its velocity is inthe +z-direction. Determine the magnitude and directionof the field.

magnetic force on a current carrying conductor
Magnetic Force on a Current Carrying Conductor
  • A force is exerted on a current-carrying wire placed in a magnetic field
    • The current is a collection of many charged particles in motion
  • The direction of the force is given by right hand rule #1
force on a wire
Force on a Wire
  • The blue x’s indicate the magnetic field is directed into the page
    • The x represents the tail of the arrow
  • Blue dots would be used to represent the field directed out of the page
    • The • represents the head of the arrow
  • In this case, there is no current, so there is no force
force on a wire cont
Force on a Wire,cont
  • B is into the page
  • The current is up the page
  • The force is to the left
force on a wire final
Force on a Wire,final
  • B is into the page
  • The current is down the page
  • The force is to the right
force on a wire equation
Force on a Wire, equation
  • The magnetic force is exerted on each moving charge in the wire
  • The total force is the sum of all the magnetic forces on all the individual charges producing the current
  • F = B I ℓ sin θ
    • θ is the angle between and the direction of I
    • The direction is found by the right hand rule, placing your fingers in the direction of I instead of
slide46

I

B

1) left

2) right

3) zero

4) into the page

5) out of the page

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

slide47

I

B

1) left

2) right

3) zero

4) into the page

5) out of the page

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

Using the right-hand rule, we see that the magnetic force must point out of the page. Since F must be perpendicular to both I and B, you should realize that F cannot be in the plane of the page at all.

torque on a current loop
Torque on a Current Loop
  • Applies to any shape loop
  • N is the number of turns in the coil
  • Torque has a maximum value of NBIA
    • When q = 90°
  • Torque is zero when the field is parallel to the plane of the loop
magnetic moment
Magnetic Moment
  • The vector is called the magnetic moment of the coil
  • Its magnitude is given by m = IAN
  • The vector always points perpendicular to the plane of the loop(s)
  • The angle is between the moment and the field
  • The equation for the magnetic torque can be written as t = mB sinq
electric motor
Electric Motor
  • An electric motor converts electrical energy to mechanical energy
    • The mechanical energy is in the form of rotational kinetic energy
  • An electric motor consists of a rigid current-carrying loop that rotates when placed in a magnetic field
quick quiz52
Quick Quiz

A square and a circular loop with the same area lie in the xy-plane, where there is a uniform magnetic field pointing at some angle θ with respect to the positive z-direction. Each loop carries the same current, in the same direction. Which magnetic torque is larger? (a) the torque on the square loop (b) the torque on the circular loop (c) the torques are the same (d) more information is needed

answer53
Answer

(c). The torque that a planar current loop will experience when it is in a magnetic field is given by . Note that this torque depends on the strength of the field, the current in the coil, the area enclosed by the coil, and the orientation of the plane of the coil relative to the direction of the field. However, it does not depend on the shape of the loop.

force on a charged particle in a magnetic field
Force on a Charged Particle in a Magnetic Field
  • Consider a particle moving in an external magnetic field so that its velocity is perpendicular to the field
  • The force is always directed toward the center of the circular path
  • The magnetic force causes a centripetal acceleration, changing the direction of the velocity of the particle
force on a charged particle
Force on a Charged Particle
  • Equating the magnetic and centripetal forces:
  • Solving for r:
    • r is proportional to the momentum of the particle and inversely proportional to the magnetic field
    • Sometimes called the cyclotron equation
particle moving in an external magnetic field
Particle Moving in an External Magnetic Field
  • If the particle’s velocity is not perpendicular to the field, the path followed by the particle is a spiral
    • The spiral path is called a helix
quick quiz57
Quick Quiz

As a charged particle moves freely in a circular path in the presence of a constant magnetic field applied perpendicular to the particle’s velocity, its kinetic energy (a) remains constant, (b) increases, or (c) decreases.

answer58
Answer

(a). The magnetic force acting on the particle is always perpendicular to the velocity of the particle, and hence to the displacement the particle is undergoing. Under these conditions, the force does no work on the particle and the particle’s kinetic energy remains constant.

hans christian oersted
Hans Christian Oersted
  • 1777 – 1851
  • Best known for observing that a compass needle deflects when placed near a wire carrying a current
    • First evidence of a connection between electric and magnetic phenomena
magnetic fields long straight wire
Magnetic Fields – Long Straight Wire
  • A current-carrying wire produces a magnetic field
  • The compass needle deflects in directions tangent to the circle
    • The compass needle points in the direction of the magnetic field produced by the current
direction of the field of a long straight wire
Direction of the Field of a Long Straight Wire
  • Right Hand Rule #2
    • Grasp the wire in your right hand
    • Point your thumb in the direction of the current
    • Your fingers will curl in the direction of the field
magnitude of the field of a long straight wire
Magnitude of the Field of a Long Straight Wire
  • The magnitude of the field at a distance r from a wire carrying a current of I is
  • µo = 4  x 10-7 T.m / A
    • µo is called the permeability of free space
amp re s law
Ampère’s Law
  • André-Marie Ampère found a procedure for deriving the relationship between the current in an arbitrarily shaped wire and the magnetic field produced by the wire
  • Ampère’s Circuital Law
    • B|| Δℓ = µo I
    • Sum over the closed path
amp re s law cont
Ampère’s Law, cont
  • Choose an arbitrary closed path around the current
  • Sum all the products of B|| Δℓ around the closed path
amp re s law to find b for a long straight wire
Ampère’s Law to Find B for a Long Straight Wire
  • Use a closed circular path
  • The circumference of the circle is 2  r
    • This is identical to the result previously obtained
example 4
Example 4

In 1962, measurements of the magnetic field of a largetornado were made at the Geophysical Observatory inTulsa, Oklahoma. If the magnitude of the tornado’s fieldwas B = 1.50 × 10−8 T pointing north when the tornadowas 9.00 km east of the observatory, what current was carriedup or down the funnel of the tornado? Model thevortex as a long, straight wire carrying a current.

example 5
Example 5

The two wires in Figure P19.40 carry currents of 3.00 Aand 5.00 A in the direction indicated. (a) Find the directionand magnitude of the magnetic field at a pointmidway between the wires. (b) Find the magnitude anddirection of the magnetic field at point P, located 20.0 cmabove the wire carrying the 5.00-A current.

practice 2
Practice 2

A long, straight wire lies on a horizontal table and carriesa current of 1.20 μA. In a vacuum, a proton moves parallelto the wire (opposite the direction of the current) witha constant velocity of 2.30 × 104 m/s at a constantdistance d above the wire. Determine the value of d. (Youmay ignore the magnetic field due to Earth.)

andr marie amp re
André-Marie Ampère
  • 1775 – 1836
  • Credited with the discovery of electromagnetism
    • Relationship between electric currents and magnetic fields
  • Mathematical genius evident by age 12
magnetic force between two parallel conductors
Magnetic Force Between Two Parallel Conductors
  • The force on wire 1 is due to the current in wire 1 and the magnetic field produced by wire 2
  • The force per unit length is:
force between two conductors cont
Force Between Two Conductors, cont
  • Parallel conductors carrying currents in the same direction attract each other
  • Parallel conductors carrying currents in the opposite directions repel each other
quick quiz73
Quick Quiz

If, in Figure 19.28, I1 = 2 A and I2 = 6 A, which of the following is true? (a) F1 = 3F2 (b) F1 = F2 or (c) F1 = F2/3

answer74
Answer

(b). The two forces are an action-reaction pair. They act on different wires and have equal magnitudes but opposite directions.

slide75

1) toward each other

2) away from each other

3) there is no force

Two straight wires run parallel to each other, each carrying a current in the direction shown below. The two wires experience a force in which direction?

slide76

1) toward each other

2) away from each other

3) there is no force

Two straight wires run parallel to each other, each carrying a current in the direction shown below. The two wires experience a force in which direction?

The current in each wire produces a magnetic field that is felt by the current of the other wire. Using the right-hand rule, we find that each wire experiences a force toward the other wire (i.e., an attractive force) when the currents are parallel (as shown).

example 6
Example 6

A wire with a weight per unit length of 0.080 N/m is suspendeddirectly above a second wire. The top wire carriesa current of 30.0 A and the bottom wire carries a currentof 60.0 A. Find the distance of separation between thewires so that the top wire will be held in place by magneticrepulsion.

magnetic field of a current loop
Magnetic Field of a Current Loop
  • The strength of a magnetic field produced by a wire can be enhanced by forming the wire into a loop
  • All the segments, Δx, contribute to the field, increasing its strength
magnetic field of a current loop equation
Magnetic Field of a Current Loop – Equation
  • The magnitude of the magnetic field at the center of a circular loop with a radius R and carrying current I is
  • With N loops in the coil, this becomes
magnetic field of a solenoid
Magnetic Field of a Solenoid
  • If a long straight wire is bent into a coil of several closely spaced loops, the resulting device is called a solenoid
  • It is also known as an electromagnet since it acts like a magnet only when it carries a current
magnetic field of a solenoid 2
Magnetic Field of a Solenoid, 2
  • The field lines inside the solenoid are nearly parallel, uniformly spaced, and close together
    • This indicates that the field inside the solenoid is nearly uniform and strong
  • The exterior field is nonuniform, much weaker, and in the opposite direction to the field inside the solenoid
magnetic field in a solenoid 3
Magnetic Field in a Solenoid, 3
  • The field lines of the solenoid resemble those of a bar magnet
magnetic field in a solenoid magnitude
Magnetic Field in a Solenoid, Magnitude
  • The magnitude of the field inside a solenoid is constant at all points far from its ends
  • B = µo n I
    • n is the number of turns per unit length
    • n = N / ℓ
  • The same result can be obtained by applying Ampère’s Law to the solenoid
slide85

If a piece of iron is inserted in the solenoid, the magnetic field greatly increases. Such electromagnets have many practical applications.

example 7
Example 7

What current is required in the windings of a long solenoidthat has 1 000 turns uniformly distributed over alength of 0.400 m in order to produce a magnetic field ofmagnitude 1.00 × 10−4 T at the center of the solenoid?

practice 3
Practice 3

It is desired to construct a solenoid that will have a resistanceof 5.00 Ω (at 20°C) and produce a magnetic field of4.00 × 10−2 T at its center when it carries a current of4.00 A. The solenoid is to be constructed from copperwire having a diameter of 0.500 mm. If the radius of thesolenoid is to be 1.00 cm, determine (a) the number ofturns of wire needed and (b) the length the solenoidshould have.

slide88

Mass Spectrometer

A mass spectrometer measures the masses of atoms. If a charged particle is moving through perpendicular electric and magnetic fields, there is a particular speed at which it will not be deflected:

slide89

All the atoms reaching the second magnetic field will have the same speed; their radius of curvature will depend on their mass.

magnetic effects of electrons orbits
Magnetic Effects of Electrons – Orbits
  • An individual atom should act like a magnet because of the motion of the electrons about the nucleus
    • Each electron circles the atom once in about every 10-16 seconds
    • This would produce a current of 1.6 mA and a magnetic field of about 20 T at the center of the circular path
  • However, the magnetic field produced by one electron in an atom is often canceled by an oppositely revolving electron in the same atom
magnetic effects of electrons orbits cont
Magnetic Effects of Electrons – Orbits, cont
  • The net result is that the magnetic effect produced by electrons orbiting the nucleus is either zero or very small for most materials
magnetic effects of electrons spins
Magnetic Effects of Electrons – Spins
  • Electrons also have spin
    • The classical model is to consider the electrons to spin like tops
    • It is actually a quantum effect
magnetic effects of electrons spins cont
Magnetic Effects of Electrons – Spins, cont
  • The field due to the spinning is generally stronger than the field due to the orbital motion
  • Electrons usually pair up with their spins opposite each other, so their fields cancel each other
    • That is why most materials are not naturally magnetic
magnetic effects of electrons domains
Magnetic Effects of Electrons – Domains
  • In some materials, the spins do not naturally cancel
    • Such materials are called ferromagnetic
  • Large groups of atoms in which the spins are aligned are called domains
  • When an external field is applied, the domains that are aligned with the field tend to grow at the expense of the others
    • This causes the material to become magnetized
domains cont
Domains, cont
  • Random alignment, a, shows an unmagnetized material
  • When an external field is applied, the domains aligned with B grow, b
domains and permanent magnets
Domains and Permanent Magnets
  • In hard magnetic materials, the domains remain aligned after the external field is removed
    • The result is a permanent magnet
      • In soft magnetic materials, once the external field is removed, thermal agitation causes the materials to quickly return to an unmagnetized state
  • With a core in a loop, the magnetic field is enhanced since the domains in the core material align, increasing the magnetic field