Transcript Electricity&… Magnetism Review of Coulomb`s Force,Magnetic

Electricity&… Magnetism
Review of Coulomb`s
Force,Magnetic Fields and
Magnetic Force
Lecture 22
Monday: 5 April 2004
Coulomb’s Law
F 
1
40
1
q1 q2
40
r2
 8.99 109 Nm 2 /C 2
Direction is determined by opposites attract
and like charges repel one another.
Electromagnetism
 fundamental force
 Interplay between electricity and magnetism
 Produces electromagnetic waves (“light”)
Electricity
 Electric fields
 Set up by electric charges
F = qE
Magnetism
 Magnetic fields
 Set up by electric currents (moving charges)
Fmag= qv x B,
v parallel to B then Fmag = 0
F = Fel + Fmag = qE + qv x B
Interaction Forces Between
Magnets
•Like poles repel, and unlike poles attract.
•Poles cannot be isolated. They occur only in
pairs, as dipoles.
Magnetic Fields
•Just as we found defining an electric field
useful, we will find defining a magnetic field
useful.
•B is the symbol for the magnetic field.
•Magnetic field lines run from north poles to
south poles.
Charges in a Magnetic Field
•Moving charges experience a force due to a
magnetic field.
FB = qv × B
•Magnitude of FB is: FB = qvB sin f
•where f is the angle between v and B.
•Direction is from the right hand rule.
Another Example
THE MAGNETIC FIELD
•B is the symbol for the magnetic field.
•Magnetic field lines run from north poles to
south poles.
Charges in a Magnetic Field
•The magnetic force on a moving charge is
perpendicular to the direction of the magnetic
field, and perpendicular to the direction of the
velocity of the charge.
•If a charge moves parallel to the direction of
a magnetic field, it experiences no magnetic
force.
A charged particle enters a uniform
magnetic field perpendicular to the field…
•Speed doesn’t change since acceleration is always
perpendicular to the direction of motion.
•Motion stays perpendicular to the field
An Example
Charges in a Magnetic Field
•If a charge moves perpendicular to a uniform
magnetic field, it will travel in a circular path.
F  ma
2
v
qvB sin f  qvB  m
r
mv
r
qB
Application
•Earth’s magnetic field shields us from
incoming charged particles. However, since
Earth’s magnetic field goes from the south
pole to the north, particles can travel parallel
to the field and enter the atmosphere near the
poles. The “aurora” is the result.
Aurora
Mass Spectrometer
•The radius of the orbit of a charged particle
depends on its mass. If we know its charge
and speed, we can determine its mass from the
radius of the orbit.
mv
qB
r
, so m 
r
qB
v
Mass Spectrometer
Mass Spectrometer
•However, if v is not known, the system can
still work, in terms of the accelerating
potential V.
2qV
qV  mv , so v 
m
1
2
2
Mass Spectrometer
mv m 2qV
Then, r 

qB qB m
2
m 2qV m2V
r  2 2

2
q B m
qB
2
2
qB 2
m
r
2V
Frequency and Period

qB
f 

2 2 m
1 2 m
T
f

qB
Angular Frequency
•Frequency or period of a circular orbit in a
magnetic field does not depend on radius.
F  ma
qvB  q rB  m r
qB  m
qB

m
2
Charges in a Magnetic Field
•Moving charges experience a force due to a
magnetic field.
FB = qv × B
•Magnitude of FB is: FB = qvB sin f
•where f is the angle between v and B.
•Direction is from the right hand rule.
An Example