Winter wk 7 – Thus.17.Feb.05
Ch.30: Changing B induces e
• Experiment with B in loops
• Define magnetic flux  Faraday’s law
• Lenz’s law for direction of induced e
• Induction & energy transfer
• Induced electric field
• Inductance of solenoids
• Energy stored in B field
Energy Systems, EJZ
Review B fields from currents I
• Right-hand rule gives
direction of B from I
 B  ds   i
0 enc
• Ampere’s law gives
magnitude of B from I
Recall B field of simple configurations
Bstraignt current
 0ienc

2 r
Bsolenoid  0 In
Bdipole on axis 
0 i R
2z3
2
Experiment with B in loops
When does the most current flow?
Predict, then measure:
(a)
(b)
(c)
(d)
When magnetic is near loop
When magnet enters loop
When magnet is inside loop
When magnet leaves loop
Define magnetic flux
Recall electric flux through a closed surface:
Electric flux   E 
 E  dA
Magnetic flux through an OPEN surface:
Magnetic flux   B   B  dA
Faraday’s law
• You observed current in loops when
magnet was moving
dB
• CHANGING magnetic flux
 e
dt
induces emf
• When is the emf greatest? Least?
Emf can drive current in conductor
e
 E  dl
Emf = voltage around a loop: e=IR
Changing magnetic flux can induce a current:
dB
 e
dt
  IR
In which loop is the greatest current induced?
Change in flux can come from
motion of loop.
d
B
dt
 e
  IR
Which loop will have the greatest emf, if they
all move into the magnetic region with the same
speed?
Practice p.816: P 2, 3, 10, 11, 14
Lenz’s law tells DIRECTION of e
Induced emf opposes change in flux:
dB
 e
dt
Induced current Ii creates an induced field Bi to
oppose any change in the external flux.
In what direction does current flow, in each diagram?
Practice with Lenz’s law
In what direction does current flow, in each loop
Reformulated Faraday’s law
Electric field = change in potential: e   E  dl
Therefore
dB
   E  ds
dt
The B field is increasing at a steady rate in all
regions. Magnitude of  E  dl
for each loop is
numbered, except loop 4 has  E  dl  0
Is B into or out of the page in shaded regions?
Motional emf
If a conductor moves through a B field, its charges
feel a Lorentz force F=qvxB.
Which direction do + move? - charges?
If charges reach equilibrium:
FE=FB
qE=qvB, so E=____
Practice p.820: P 29, 31
(See rate of energy transfer on next slide.)
Work done by motion or current in B field?
dWork d ( F  dx )
Power 

 Fv
dt
dt
Force  IL  B  ILB
d  B d ( BA)
d ( Lx)
Induced emf :

B
 BLv
dt
dt
dt
Find induced current from e  IR 
dB
dt
I ( B , L, v , R ) 
F ( B , L, v , R ) 
BLV 

P
R
2
Inductance = Flux/current
Inductance L 
B
I
so flux  B  LI
dB
dI
Sub in Faraday ' s Law : e 
L
dt
dt
Power  I e  rate of change of magnetic energy
dU B
dI
 I e  LI . Integrate to find
dt
dt
dU B
dI
UB  
dt   LI dt  L  I dI
dt
dt
UB 
Magnetic energy density
Inductance of solenoid L=NBA/I=(nl)A(0In)/I=_
Magnetic energy density = energy/volume
2
1
UB
2 LI
uB 

 ______________
volume
Al
Sub in B   0 In to find
2
B
uB 
20
This is true in general, not just for solenoid.
Practice: P.95 (p.825)
Applications to Sun and Earth
A coronal mass ejection sends a blob of
magnetized plasma toward Earth, where it
decreases the local magnetic field by 1% in 0.5s.
Find the magnitude of the induced emf in a square
segment of the electrical grid 100 km on each
side.
How big a current could this CME drive in the grid
segment, through copper wire 4 cm in diameter?