Electricity&… Magnetism
Review of Coulomb`s
Force,Magnetic Fields and
Magnetic Force
Lecture 22
Monday: 5 April 2004

Coulomb’s Law
F

1 q
1
4
 r
0
2 q
2
1
4

0

8 .
99

10
9
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 = q E
Magnetism

Magnetic fields

Set up by electric currents (moving charges)
F mag
= q v x B, v parallel to B then F mag
= 0
F = F el
+ F mag
= q E + q v 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.
F
B
= qv
×
B
•Magnitude of
F
B is: F
B
= 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 qvB sin f  qvB
 m v 2 r r
 mv 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.
r r , so m r r

Mass Spectrometer

Mass Spectrometer
•However, if v is not known, the system can still work, in terms of the accelerating potential V .
qV
 mv , so v
2 qV

Mass Spectrometer
Then, r r
 mv
 r r
2 2
2 qV
2 V r r

Frequency and Period f f

2


2

 f f
1

2


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 r qB
 m


Charges in a Magnetic Field
•
Moving charges experience a force due to a magnetic field.
F
B
= qv
×
B
•Magnitude of
F
B is: F
B
= qvB sin f
•where f is the angle between v and B .
•Direction is from the
right hand rule.

An Example