2. Magnetism
âą Magnetic Force and Magnetic Field
âą How are Force and Field related?
âą What is the Source of the Field?
Apr 3 2002
3. Force on moving charge
âą Charged particle in a combination of Electric
and Magnetic Field:
FL = q E + qv x B
This we know!
Apr 3 2002
Lorentz Force
Direction:Right-Hand Rule
4. Force on moving charge
-q FE
v
E
xB
FB
In B-Field:
F= m a
|q| v B = m v2/R
-> R = m v/(q B)
FL = q E + q v x B
Apr 3 2002
Cyclotron Radius
5. Example
1 mile
âą Why so big?
RHIC
R = m v/(q B)
Momentum p
âą Large p -> Large R
âą B ~ 10T (very big!)
âą Max. B in Lab around 100 T
Relativistic Heavy Ion Collider
Apr 3 2002
6. Work done on moving charge
-q FE
v
E
xB
FB
L
W = FE L
=qEL
Apr 3 2002
dW = FB dL = (q v x B) dL
=0
7. Magnet and Current
Wire
F
F
I
âą Force on wire if I != 0
âą Direction of Force depends on Sign of I
âą Force perpendicular to I
Apr 3 2002
8. N
Wire, I > 0
N
S
Apr 3 2002
S
X
N
S
Currents and Magnetic Field
9. Currents and B-Field
I
âą Current as Source of B
âą Magnetic Field lines
are always closed
â no Magnetic Charge
(Monopole)
âą Right Hand Rule
Apr 3 2002
14. Magnetic Field vs Electric Field
B
r
+Q
v
B
~q
~1/r2
~v x r
azimuthal
B = ”0/(4 Ï) Q/r2 v x r
”0 = 4 Ï 10-7 T m /A
Apr 3 2002
E
~q
~1/r2
/
radial
E
+Q
E = 1/(4 Ï Î”0) Q/r2 r
Δ0 = 8.85 10-12 C2/(Nm2)
16. Magnetic Field for Current I
B = ”0/(4 Ï) Q/r2 v x r
for single charge
I = dQ/dt -> dQ v = dQ dl/dt = I dl
dB = ”0/(4 Ï) I dl x r/r2
Law of Biot-Savart:
Magnetic Field dB for current through segment dl
Apr 3 2002