1. Chapter30: Electromagnetic Induction
Motional EMF’s
Conductor Moving through a magnetic field
Magnetic Force on charge carriers
Accumulation of charge
Balanced Electrostatic/Magnetic Forces
qvB=qE
Induced Potential Difference
E = EL = vBL
Generalized
d E = v ´B×dl
F = qv ´B

2. With conduction rails:
F = qv ´B I
demonstrations with galvanometer
moving conductor
moving field!

3. I
Consider circuit at right with total circuit resistance of 5 W, B = .2 T, speed of conductor = 10 m/s, length of 10 cm. Determine:
(a) EMF,
(b) current,
(c) power dissipated,
(d) magnetic force on conducting bar,
(e) mechanical force needed to maintain motion and
(f) mechanical power necessary to maintain motion.
dE = v ´B×dl

4. dl=dr I w B

5. Faraday’s Law of Induction
Changing magnetic flux induces and EMF
Lenz’s Law: The direction of any magnetic induction effect (induced current) is such as to oppose the cause producing it.
(opposing change = inertia!)

6. A E B
(increasing) B
(decreasing) A E A E B
(increasing) A E B
(decreasing)

7. Conducting rails: changing flux from changing area
dA=l vdt

8. Simple Alternator
q = w t B w

9. Example: A coil of wire containing 500 circular loops with radius 4
Example: A coil of wire containing 500 circular loops with radius 4.00 cm is placed in a uniform magnetic field. The direction of the field is at an angle of 60o with respect to the plane of the coil. The field is decreasing at a rate of .200 T/s. What is the magnitude of the induced emf?
60o

10. A “new” lab experiment
I=I0 sin(wt) r
F = B(r,t)

11. Eddy Currents
Induced currents in bulk conductors
magnetic forces on induced currents
energy losses to resistance
ex: Conducting disk rotating through a perpendicular magnetic field
Ferromagnets ~ Iron (Electrical Conductor)
Constrain Eddy currents with insulating laminations

12. Induced Electric Fields
B (increasing)
Changing magnetic Flux produces an EMF E
Induced Electric Field E
Not an Electrostatic field
Not Conservative!

13. I’ induced E
I’ induced E B
increasing I I
increasing

14. Maxwell’s Equations
Lorentz Force Law

15. zero resistivity below Tc (with no external magnetic field)
Superconductivity
zero resistivity below Tc
(with no external magnetic field)
with field above the critical field Bc, no superconductivity at any temperature B Bc
Normal
Superconducting T Tc

16. More magnetic fun with superconductivity: the Meissner Effect
Within a superconducting material, Binside = 0!
magnetic field lines are expulsed from superconductor
Relative permeability Km = 0
internal field is reduced to 0
=> Superconductor is the perfect diamagnetic material!

17. mechanical effects
ferromagnetic or paramagnetic materials attracted to permanent magnet
superconductor repels permanent magnet!
Type-II superconductors
small filaments of “normal phase” coexist within bulk superconductor
some magnetic field lines penetrate material
two critical fields field just begins to penetrate material
Bc1 : magnetic field just begins to penetrate material
Bc2 :bulk material ”goes normal”
more practical for electromagnets: higher Tc and Bc2