1. Last time Result of Cross Product is Perpendicular to both and
MAGNETIC FORCE
point charge
Result of Cross Product
is Perpendicular to both and
Right-Hand Rule: 2) 1)

2. Today
Magnet force on currents
Hall effect
Relativity effect

3. iClicker Question
Small metal ball has charge q = +0.05C and mass, m = 0.025kg. Ball enters a region of magnetic field B = 0.5 T that is perpendicular to its velocity v = 200m/s. Centripetal acceleration = v2/r. What is radius of the curve ball will move thru in magnetic field?
200m
100m
250m
120m
50m . A

4. .
a) F = qv1B = (0.05)(200)(0.5) = 5N
b) (see diagram) Force in –z direction
c) F = ma = qv1B = 5N
a = 5N/0.025kg = 200 m/s2
d) v2/r = 200m/s2 , r = v2/(200m/s2) = (200m/s)2/200m/s2 = 200m

5. Biot-Savart Law BIOT-SAVART LAW point charge We need to understand
how these are related
BIOT-SAVART LAW
point charge
BIOT-SAVART LAW
current in a wire
Blast from the Past:
Lecture 12
= length of this
chunk of wire

6. GOAL: Show (point charge) (wire) (POSITIVE) POINT CHARGE MANY POINT
CHARGES
N particles
particles per
volume ΔV ΔV
Move the vector symbol
CHUNK
OF WIRE
= length of this
chunk of wire
Blast from the Past:
Lecture 12

7. Magnetic Force on a charge or wire
point charge
We just showed how
these are related
MAGNETIC FORCE
current in a wire
= length of this
chunk of wire

8. Magnetic Force on a Wire
Current-carrying wire in an applied magnetic field B
Bapplied
Bapplied I
Which way will the wire move?

9. Very Close to the Wire B I Very close to the wire: r << L B I
Blast from the Past:
Lecture 13

10. iClicker question: Two long parallel wires carry currents of 5 A and 10 A in the same direction as shown. What is the direction of the magnetic force acting on the 10-A wire?
Perpendicular to the plane of the page and into the page
Perpendicular to the plane of the page and out of the page
Downward
Inward toward the other wire
Outward away from the other wire d

11. Force Between Parallel Wires
Bapplied = Magnetic field applied by the red wire.
Blue wire feels a force down.
Fon blue wire
Bapplied I
Bapplied I
What about reciprocity? (Equal and opposite forces)

12. iClicker question: Two long parallel wires carry currents of 5 A and 10 A in opposite directions as shown. What is the direction of the magnetic force on the 10-A wire?
Perpendicular to the plane of the page and into the page
Perpendicular to the plane of the page and out of the page
Upward
Downward
Outward away from the other wire e

13. Force Between (Anti) Parallel Wires
Bapplied = Magnetic field applied by the red wire.
Blue wire feels a force up. x
Bapplied
Fon blue wire I x
Bapplied x
Bapplied I
Fon red wire x
Bapplied
Bapplied = Magnetic field applied by the blue wire.
Red wire feels a force down.

14. Hall Effect By measuring the Hall effect for a particular material,
we can determine the sign of the moving particles
that make up the current
Why would it be anything other than electrons? (Negative charges)
Semiconductors: sometimes current is carried by electrons,
but sometimes it is carried by the "holes".
In semiconductors, "holes" (missing electrons)
in the electron sea behave like positive charges.

15. Hall Effect Inside a Material: Bapplied Bapplied - - - - - - - - - - -
MAGNETIC FORCE
point charge
A hole in the electron sea
behaves like a proton.
Inside a Material:
Moving holes
get pushed
to the top
Proton
or "Hole" x
Bapplied x
Bapplied
Electron
EC got here
Moving electrons
get pushed
to the bottom

16. Hall Effect Inside a Material: ΔV = Hall Voltage - - - - - - - - - - -
MAGNETIC FORCE
point charge
A hole in the electron sea
behaves like a proton.
Inside a Material:
Moving holes
get pushed
to the top
 Until the Hall Voltage
is strong enough to balance
the magnetic force
ΔV = Hall Voltage
How long does this go on? x
Bapplied
EC got here
Moving electrons
get pushed
to the bottom

17. Measuring the Hall Effect
1. Apply B-Field
2. Apply Current I
3. Measure "Hall Voltage"
EC got here

18. Currents Due to Magnetic Forces
Metal bar
polarization Fm
How much force do we
need to apply to keep
the bar moving at constant
speed?
What is direction of E?

19. Moving Bar and Energy Conservation
P=IV=I(emf)
Are we getting something for nothing?
Bar – current I: FI F Fm
Work:
Power: x
Main principle of electric generators:
Mechanical power is converted to electric power

20. Reference Frame Any magnetic field? charged tape
What is direction of E?
No work done – static equilibrium, net force is zero.

21. iClicker Question charged tape
Jessie
Jack
In case Jack have two positively changed tapes side by side. For the interaction between the two tapes :
A). Jack and Jessie: purely through E force.
B). Jack: only through E force. Jessie: only through B force.
C). Jack and Jessie: through a mixture of B and E forces.
D). Jack: though only E forces. Jessie: through a mixture of B and E forces.
What is direction of E?
No work done – static equilibrium, net force is zero.

22. Magnetic Forces in Moving Reference Frames
Electric force: (assume independent of frame?)
Two protons +e r 1 2 v
Magnetic field:
F21,m B1
Magnetic force:
F21,e E1
Coulomb force on moving charges: approximation, E is not exactly the same (address later). Recall that we have already said that two current carrying wires experience an attractive magnetic force if current direction is the same.

23. Magnetic Forces in Moving Reference Frames
Electric force: +e r 1 2 v E1
F21,e B1
F21,m
Magnetic force:
Ratio:
Coulomb force on moving charges: approximation, E is not exactly the same (address later)

24. Magnetic Forces in Moving Reference Frames1 2 v E1
F21,e B1
F21,m
For v<<c the magnetic force is much
smaller than electric force
How can we detect the magnetic force on
a current carrying wire?
Ask students to reconcile this with the fact that two wires carrying current in the same direction are attracted to each other.
Full Lorentz force:
downward

25. Magnetic Forces in Moving Reference Frames
20 ns +e r 1 2 v E1
F21,e B1
F21,m
15 ns
Who will see protons hit
floor and ceiling first?
Time must run slower in moving frame.
Einstein 1905:
“On the electrodynamics of moving bodies”
This is a kind of phenomenon which led Einstein to develop theory of relativity
Twin paradox

26. Relativistic Field Transformations
Our detailed derivations are not correct for relativistic speeds,
According to the theory of relativity:

27. Magnetic Field of a Moving Particle
Still:
Moving:
Slow case: v<<c 
Field transformation is consistent with Biot-Savart law
What about B below particle?
Electric and magnetic fields are interrelated
Magnetic fields are relativistic consequence of electric fields

28. Electric Field of a Rapidly Moving Particle
For a single charged particle Ex, Ey, Ez are different when moving rapidly.

29. Interpretation depends on reference framev
Uniform B field in lab frame. For observers in the metal bar rest frame, the charge build up because of non-zero E fieid. For lab frame observers, the charge is build up by magnetic force.