Download slides

Physics 272
February 23
Spring 2017
http://go.hawaii.edu/j8M
Prof. Philip von Doetinchem
[email protected]
PHYS272 - Spring 17 - von Doetinchem – II/41
Magnetic force
●
●
●
●
●
●
A moving charge or a current creates a magnetic field in the
surrounding space (in addition to electric field)
The magnetic field exerts a force on any other moving charge or
current that is present in the field.
Magnitude of the force is proportional
to amount of charge
Magnitude of the force is proportional
to the magnetic field strength.
Magnitude of the force is proportional
to the velocity
Force is perpendicular to the velocity and
magnetic field
Right hand rule
Force (direction
of deflection)
magnetic
field B
velocity v
PHYS272 - Spring 17 - von Doetinchem – II/42
Magnetic field lines and magnetic flux
●
●
●
●
●
●
Magnetic field lines work in a
similar way as for the electric
field
Tangents on field lines
represent direction of magnetic
field
Higher density of lines
represents a higher magnetic
field
Source: http://physics.stackexchange.com
Magnetic field lines never intersect
Magnetic field lines are always closed: they are not
starting or ending
Be careful: magnetic force is not in the direction of
magnetic lines → it is perpendicular to B and velocity
PHYS272 - Spring 17 - von Doetinchem – II/43
Magnetic flux and Gauß's law for magnetism
●
Magnetic flux B describes
the number of field lines
poking through an area A
●
●
●
No equivalent to electric charge
exist in magnetism!
No magnetic monopoles = total
magnetic flux through a closed
surface is always zero.
Gauß's law for magnetism:
Wilhelm Weber
1804-1891
Source: http://de.wikipedia.org/wiki/Wilhelm_Eduard_Weber
PHYS272 - Spring 17 - von Doetinchem – II/44
Motion of charged particles in a magnetic field
●
●
●
●
●
●
Charged particles in magnetic field follows Newton's law
Example: uniform
magnetic field into the
plane
Charged particle is
kept on a circle
Magnetic forces point
all towards the center
Force is always perpendicular to velocity
→ cannot change the magnitude of the velocity
→ can only change direction
Magnetic force can never do work on charged particle
in any type of magnetic field → velocity stays constant
PHYS272 - Spring 17 - von Doetinchem – II/45
Motion of charged particles in a magnetic field
●
●
Centripetal acceleration equals magnetic force:
If the velocity is not perpendicular to magnetic field
→ particle moves on a helix
PHYS272 - Spring 17 - von Doetinchem – II/46
geographic North Pole
magnetic South Pole
geographic South Pole
magnetic North Pole
PHYS272 - Spring 17 - von Doetinchem – II/47
Magnetic bottle
●
●
●
●
Radiation belts around
the Earth trap charged
particles
Near the poles radiation belt
particles can interact with
atmosphere and can cause
colorful light emissions
non-uniform B field
Magnetic force points away
from denser region
Angle between drift velocity
and field lines changes and
can cause the particle to
reverse direction
Source: http://de.wikipedia.org/wiki/Van-Allen-G%C3%BCrtel
http://youtu.be/FcfWsj9OnsI
PHYS272 - Spring 17 - von Doetinchem – II/48
Velocity selector
PHYS272 - Spring 17 - von Doetinchem – II/49
Mass spectrometers
●
Use velocity filter
●
Leave filter and continue in region with magnetic field only
●
Ions are deflected in a circle
●
Used to measure masses of ions → higher masses have a
larger radius
PHYS272 - Spring 17 - von Doetinchem – II/50
Magnetic force on a current-carrying conductor
●
Average force on each charge:
●
Total force on all moving charges
PHYS272 - Spring 17 - von Doetinchem – II/52
Magnetic force on a current-carrying conductor
●
●
●
General case: B field is not perpendicular to wire:
Non-straight wire → divide into infinitesimally small
sections:
Negative charges move the opposite direction and
the force goes in the same direction as for positive
charges
PHYS272 - Spring 17 - von Doetinchem – II/53
Loud speaker
●
●
●
●
●
Radial magnetic field of
permanent magnets
exerts force on voice coil
Source: http://en.wikipedia.org/wiki/Loudspeaker
radial magnetic field
Current in voice coil depends
on the signal from the
amplifier
Direction of current decides
the direction of the force
Speaker cone starts vibrating
Volume knob turns up the
current amplitude
current along
voicecoil
voicecoil
suspension
diaphragm
PHYS272 - Spring 17 - von Doetinchem – II/54
Force and torque on a current loop
0
●
●
Current-carrying conductors often form closed loops
Example: rectangular loop in a uniform magnetic
field
–
The total force on the
loop is zero
–
But the total torque
is generally not zero

PHYS272 - Spring 17 - von Doetinchem – II/55
Force and torque on a current loop
PHYS272 - Spring 17 - von Doetinchem – II/56
Magnetic torque: vector form
only valid for uniform
magnetic field
●
●
●
Greatest torque when magnetic dipole moment and
magnetic field are perpendicular
Torque is zero when magnetic dipole moment and
magnetic field are (anti)parallel
Analogue to electric dipole moment and electric field
PHYS272 - Spring 17 - von Doetinchem – II/57
Potential energy for a magnetic dipole
●
●
●
●
●
If magnetic dipole changes orientation in magnetic field
→ the field does work on it
In analogy to the potential energy of an electric dipole
→ potential energy for a magnetic dipole:
Potential energy is zero when magnetic dipole moment is
perpendicular to the field
torque tries to align magnetic dipole moment and magnetic
field
Derived equations are also true for any type of plane loop
and not only for rectangular loops
PHYS272 - Spring 17 - von Doetinchem – II/58
Magnetic torque: loops and coils
●
●
●
Solenoid:
helical winding of wire
Close spacing of
windings
→ approximate as circular loops
Total magnetic torque of a
solenoid in a uniform magnetic
field is just the sum of the torque
of the individual windings:
magnetic dipole
moment of one
winding
●
Angle between axis of
solenoid and magnetic field
Solenoids are important as source of magnetic fields
PHYS272 - Spring 17 - von Doetinchem – II/59
The direct-current motor
●
Magnetic torque is converted into mechanical energy
●
Direct current motor:
–
Loop in a magnetic field
–
Magnetic dipole moment is
generated by external
current source every time
the current loop aligns with
the magnetic field
–
Torque is created and loop
starts spinning
–
After spinning 180deg
→ magnetic dipole moment is
reversed with respect to the
loop, but stays the same with
respect the magnetic field
→ loop continues to spin in the same direction
PHYS272 - Spring 17 - von Doetinchem – II/60
Magnetic force on a curved conductor
PHYS272 - Spring 17 - von Doetinchem – II/61
Magnetic force on a curved conductor
1
PHYS272 - Spring 17 - von Doetinchem – II/62
Magnetic force on a curved conductor
B
B
B
PHYS272 - Spring 17 - von Doetinchem – II/63