5. Magnetostatics
The force is generatedby the magnetic field B.
Early evidence for the magnetic field.
Magnetic Field
Bar magnet Magnetic field lines
Magnetic Field of the Earth
Direction measuredby a compass.
Oersted, in 1820 What he saw.
Qersted’s experiment, modern version
Biot and Savert found that the force on a compass encirclesa wire. Formulated the Biot-Savert law.
Ampere stated that all magnetic field are generated by currents.The elementary magnetic dipoles are current loops.
The force is generatedby the magnetic field B.
How does the field acton the moving charge?
How is the field generatedby the moving charges?
)( BvEF Q
Total force on a charge:
Lorentz’s law:
Right – hand rule
Magnetic force on a moving charge:
)( BvF Qmag
Example 5.2 – Cyclotron Motion
Cloud Chamber
1.6 MeV proton
7 MeV alpha
The Cylcotron
O. E. Lawrence M. S. Livingston 1934
Van Allen Belts
Protons and electrons from the solar wind are trapped bythe earth’s magnetic field.
Currents
Line current I 1 A = 1 C/s
)( BlF dImag
Magnetic forces do not work!
0)( dtQddW magmag vBvlF
Example 5.3
B points into the page.
Surface current density
vK
dadamag )()( BKBvF
Volume current density
vJ
ddmag )()( BJBvF
t
Jcontinuity equation:
Biot-Savart Law
Magnetostatics:
Steady currents 00
JJ
t
22
ˆ'
4'
ˆ
4)(
r
r
r
r lIrB
dIdl oo
Magnetic field of a steady line current
27 /104 ANo
Permeability of free space – defines the unit Ampere
Superposition principle for the magnetic field gives the differentversions of the Biot-Savart law.
'ˆ
4)( 2 dlo
r
rIrB
line current
'ˆ
4)( 2 dao
r
rKrB
surface current
'ˆ
4)( 2
do
r
rJrBvolume current
cvqo
for only
)ˆ(
4)( 2
r
rvrB
Moving point charge