PHYS 2421 - Fields and Waves
Magnetism: the idea
Remember Coulomb’s law:
q1
F
F
r
q2
F =k
q1q2
r2
Now put q1 in motion
q2 feels a force
changing in
magnitude and
direction
This is the origin of magnetism and it is produced by
moving charges and affect only moving charges
PHYS 2421 - Fields and Waves
In chapter we will study:
• Permanent magnets
• Magnetic fields
• Effect of magnetic fields
• on charges
• on currents
• on loops (torque)
Background:
• 1st record of magnetic iron ore appeared in Magnesia 2500 years ago
• Shen Kuo was the first scientist to use magnetic needles in navigation
• H.C. Ørsted studied relation between electricity and magnetism,
followed by Ampere, Gauss and Faraday.
• Maxwell synthesize his equations combining electricity and
magnetism
• Einstein’s theory of relativity show that electricity is the
same as magnetism in a different frame of reference
A few facts:
• Magnets have poles, usually called north or south
• Equal poles repel, unequal poles attract
• Magnets attract some un-magnetized metals
• There are no single poles
• Ørsted: electric currents deflect compasses like magnets
• The earth has a
magnet but its N and
S are opposite to the
geographical north
and south
Remember the electric case
Follow a similar approach for the magnetic case
A few facts:
•A moving charge creates a magnetic field
•The magnetic field, B, exerts forces on other moving charges
•The force is given by F  qv  B
where v is the velocity of the moving charge
•The magnitude is given by F  q vB sin 
where  is the angle between V and B
•The units of the magnetic field are
 F 
N
N
N


 Tesla
 B    
 qV  C  m/s  m  C/s  Am
Some examples
F  qv  B  F  q vB sin 



F  1.6 1019 C 3 105 m/s  2 T  sin 300
 4.8 1014 N
In negative y direction
Homework : Problem 27.1 and 27.7 (11th Ed.) or
27.1 and 27.5 (12th Ed.)
Summary of Section 27.2
The force produced by a magnetic field B on a
charge q moving at velocity is:
F  qv  B
Its magnitude is:
F  q vB sin 
N
and B is measured in units of: Tesla 
Am
Hmwk Section 27.2:
Problems 27.1 and 27.7 (11 th Ed.) or
27.1 and 27.5 (12th Ed.)
In electric case E and F are parallel or antiparallel
F  qE
In the magnetic case B is always perpendicular to F
F  qv  B
Thus, the magnetic B lines are not “force lines
Some examples of direction of B fields
More examples of direction of B fields
Notice that all B lines close on itself
Now calculate magnetic flux over an area A:
B  B  A
For closed surfaces, since all B lines close on
itself, the flux will be zero
 B   B  dA  0
Magnetic version of Gauss law
Units:
Weber
Wb = T x m2
 B  B  A  BA cos600
B
0.9  103 Wb
B

6T
0
4
2
A cos60  3  10 m   0.5
Homework : Problems 27.11 and 27.12 (11th Ed.) or
27.11 and 27.12 (12th Ed.)
Soln P. 12: a) 0, b) -0.0115Wb, c) b) +0.0115Wb d) 0
Summary of Section 27.3
B field lines
Magnetic flux
B  B  A
 B   B  dA  0
Hmwk Section 27.3: Problems 27.11 and 27.12 (11 th Ed.) or
27.11 and 27.12 (12th Ed.)