Download Magnetic Fields and Forces

Chapter 27
Magnetic Field and
Magnetic Forces
PowerPoint® Lectures for
University Physics, Thirteenth Edition
– Hugh D. Young and Roger A. Freedman
Lectures by Wayne Anderson
Copyright © 2012 Pearson Education Inc. Modified 2016 Scott Hildreth Chabot College
Goals for Chapter 27
• Study magnets & forces they exert
on each other
• Calculate force a magnetic field
exerts on a moving charge
• Contrast magnetic field lines with
electric field lines
• Analyze motion of a charged
particle in a magnetic field
Goals for Chapter 27
• See applications of magnetism in
physics and chemistry
• Analyze magnetic forces on
current-carrying conductors
• Study the behavior of current
loops in a magnetic field
Introduction
• How does magnetic resonance
imaging (MRI) allow us to see
details in soft nonmagnetic
tissue?
• How can magnetic forces,
which act only on moving
charges, explain the behavior
of a compass needle?
Magnetic poles
• Forces between
magnetic poles mimic
forces between
charges.
Magnetism and certain metals
• BUT….either pole
of a permanent
magnet will attract a
metal like iron??
Magnetic field of the earth
Magnetic monopoles
• Breaking a bar
magnet does not
separate its poles
• There is no
experimental
evidence for
magnetic
monopoles.
Electric current and magnets
• (1820) Hans Oersted
discovered wire carrying
current causes compass
to deflect.
• There is a connection
between moving charges
and magnetism.
Hans Oersted
• Father owned a pharmacy
• Brother became prime
minister of Denmark
• Received 3-year travel
grant to explore science in
Europe
• Accomplished in more
than physics!
•
•
Thesis based on Kant:
“Architectonics of
Natural Metaphysics”
First to produce pure
aluminum
The Oersted
Medal for
teaching of
physics!
Electric current and magnets
• RIGHT-HAND RULE
applies to identify
direction of magnetic
field from currentcarrying wire!
Right Thumb in direction of current
Right Hand Fingers curl in direction
of Magnetic field!
Electric current and magnets
• We’ll find a RIGHTHAND RULE applies to
identify the direction of a
magnetic field from a
current-carrying wire!
Right Thumb in direction of
current
Right Hand Fingers curl in
direction of Magnetic field!
The magnetic field
• A moving charge (or current) creates a magnetic field in
the surrounding space.
The magnetic field
• Magnetic fields denoted with letter “B”
• measured in Tesla or Gauss (10-7 Tesla)
The magnetic field
• Magnetic fields denoted with letter “B”
• measured in Tesla or Gauss (10-4 Tesla)
• Tesla =
Newton-second
Coulomb-meter
• Tesla =
Newton/Amp-meter
The magnetic field
• A magnetic field exerts a force on any other moving
charge - or current - that is present in the field.
The magnetic force on a moving charge
• Magnetic force on moving charge q
is perpendicular to both
•
velocity vector direction of q
and
•
magnetic field.
• Magnitude of magnetic force is
F = |q|vB sin.
Magnetic force as a vector product
•
Write magnetic force as vector cross product
•
Right-hand rule gives direction of force on positive charge.
Magnetic force as a vector product
•
Write magnetic force as vector cross product
•
Left-hand rule gives direction of force on negative charge.
Equal velocities but opposite signs
• Two charges of equal magnitude but opposite signs
moving in same direction in same field
experience magnetic forces in opposite directions.
Cathode Ray Tubes!
•
The first computer “monitors”
Determining the direction of a magnetic field
• Cathode-ray tube shows direction of magnetic field
Magnetic force on a proton
• Beam of protons (q =+1.6 x 10-19C) moves at 3.0 x 105 m/s
through 2.0 Tesla field directed along z axis.
Velocity direction is 30 degrees from the z axis in the x-y plane.
Force on a proton?
Magnetic force on a proton
• Beam of protons (q =+1.6 x 10-19C) moves at 3.0 x 105 m/s
through 2.0 Tesla field directed along z axis.
Velocity direction is 30 degrees from the z axis in the x-y plane.
Force on a proton?
• F = qv x B = (1.6 x 10-19 C) x (3 x 105 m/s) x (2 T) x sin (30)
•
= 4.8 x 10-14 N
Magnetic field lines
Magnetic field lines are not lines of force
• Important! Remember magnetic field lines are not lines of
magnetic force.
Magnetic flux
Magnetic flux calculations
• Flux through flat surface of area 3.0 cm2 = +0.90 mWb
• “mWb = “milli-Webers”
• What is B field and direction of A?
Magnetic flux calculations
• Flux through flat surface of area 3.0 cm2 = +0.90 milliWb.
• What is B field and direction of A?
• Flux FB = BA cos  = +0.90 milliWb
• A = 3.0 cm2 = 3.0 x 10-4 m2 and  = 60°
• B = 6.0 Teslas
Motion of charged particles in a magnetic field
• Charged particle in magnetic
field (only) moves with
constant speed
•
F = qv x B
•
Force is PERPENDICULAR
to v
•
So is acceleration!
•
No change in magnitude
of velocity!
Motion of charged particles in a magnetic field
• If velocity of particle is ONLY
perpendicular to B field,
particle moves in a circle of
radius R = mv/|q|B.
• Number of revolutions of
particle per unit time is
cyclotron frequency.
Motion of charged particles in a magnetic field
• F = qvB = mv2/R
w = v/R = qB/m
f = w/2p
Motion of charged particles in a magnetic field
• If velocity of particle is
perpendicular to B field,
particle moves in a circle of
radius R = mv/|q|B.
• IF add a “kick” to speed,
Radius increases!
• A cyclotron!
• Number of revolutions of
particle per unit time is
cyclotron frequency.
The “father” of cyclotrons! Ernest Lawrence
Motion of charged particles in a magnetic field
Motion of charged particles in a magnetic field
• Magnetron in Microwave Oven!
Motion of charged particles in a magnetic field
• Magnetron in Microwave Oven!
Motion of charged particles in a magnetic field
• Magnetron in Microwave Oven!
Motion of charged particles in a magnetic field
• Magnetron in Microwave Oven!
Helical motion
• If particle has velocity
components parallel to and
perpendicular to B field, its
path is a helix.
• Speed & kinetic energy still
particle remain constant.
A nonuniform magnetic field
•
Charges can be trapped in a
magnetic bottle, which results from
a non-uniform magnetic field.
•
Van Allen radiation belts act like a
magnetic bottle, and produce
aurora. These belts are due to the
earth’s non-uniform field.
Bubble chamber
• Track of charged particles
in a bubble chamber
experiment.
Velocity selector
• Velocity selectors use
perpendicular electric &
magnetic fields to select
particles of specific
speed from beam.
• Only particles having
speed v = E/B pass
through undeflected.
Thomson’s e/m experiment
• Measure ratio e/m for electron.
Mass spectrometer
•
Mass spectrometer measures
masses of ions.
•
Bainbridge mass spectrometer
first uses velocity selector,
then
magnetic field separates particles
by mass.
The magnetic force on a current-carrying conductor
•
Magnetic force on a moving positive
charge in a conductor.
•
F = Il x B = ILB sin 
•
dF = Idl x B for a segment dl
• VECTORS!
•
•
I = scalar current (amps)
•
l = direction of current
•
B = direction of Mag. Field.
Magnetic force is perpendicular to the
wire segment and the magnetic field.
Magnetic force on a straight conductor
• Example 27.7
A straight horizontal copper rod carries a
current of 50.0 A from west to east in a
region between the poles of a large
electromagnet. In this region there is a
horizontal magnetic field towards the
northeast (45 degrees north of east) with
magnitude 1.20 T.
Magnetic force on a straight conductor
• Example 27.7
A straight horizontal copper rod carries a
current of 50.0 A from west to east in a
region between the poles of a large
electromagnet. In this region there is a
horizontal magnetic field towards the
northeast (45 degrees north of east) with
magnitude 1.20 T.
• What is F on the segment?
• What is the maximum possible force if it
changes direction?
Magnetic force on a straight conductor
• Example 27.7
A straight horizontal copper rod carries a
current of 50.0 A from west to east in a
region between the poles of a large
electromagnet. In this region there is a
horizontal magnetic field towards the
northeast (45 degrees north of east) with
magnitude 1.20 T.
• What is F on the segment?
• What is the maximum possible force if it
changes direction?
Magnetic force on a straight conductor
• Example 27.7
A straight horizontal copper rod
carries a current of 50.0 A from
west to east in a region
between the poles of a large
electromagnet. In this region
there is a horizontal magnetic
field towards the northeast (45
degrees north of east) with
magnitude 1.20 T.
•
What is F on the segment?
•
What is the maximum possible
force if it changes direction?
How do we solve physics
problems?
- SKETCH it
- COMB through the
problem; pickout key data
points and concepts
- Set up what is known,
and what is needed!
Magnetic force on a straight conductor
A straight horizontal copper rod carries a current of 50.0 A
from west to east in a region between the poles of a large
electromagnet.
50.0 A
W
E
Magnetic force on a straight conductor
• What is Force on the current segment from the
magnetic field?
• What is the maximum possible force if it changes
direction?
Magnetic force on a straight conductor
• F = iL x B = iLB (sin q)
• Direction of F is perpendicular to both (Right-Hand Rule)
Magnetic force on a straight conductor
• F = iL x B = iLB (sinq)
• If F = mg, current is large enough to hold up conductor
Magnetic force on a curved conductor
• Look at Example 27.8!
• What is the TOTAL magnetic force on this wire?
Loudspeaker
• Loudspeaker design.
• If current in the voice coil oscillates, speaker cone oscillates
at the same frequency.
Force and torque on a current loop in B field
•
Net force on a current loop in a uniform magnetic field is zero.
•
But the net torque is not, in general, equal to zero.
Force and torque on a current loop
•
Net force on a current loop in a uniform magnetic field is zero.
•
But the net torque is not, in general, equal to zero.
Force and torque on a current loop
•
Net force on a current loop in a uniform magnetic field is zero.
•
But the net torque is not, in general, equal to zero.
The direct-current motor
• Direct-current motor.
The direct-current motor
• Direct-current motor.
The direct-current motor
• Direct-current motor.
The direct-current motor
• Direct-current motor.
Real life!
• Inertia of coil
• Resistance of wire
• Eddy effects of nonlinear magnetic field
• Load on shaft
Magnetic torque & magnetic moment
• Right-hand rule to
determines direction of
magnetic moment
(turning force = torque)
on current loop.
Magnetic torque and potential energy of a coil
• Potential energy of magnetic dipole in a magnetic field.
How magnets work
How magnets work
The Hall Effect
• Hall effect