Transcript Announcements

Magnets and Charges
Vector Direction Conventions
Left
Right
Up
Down
In
Out
Magnetic Force on a Charge
F = qv  B
Source: Griffith, The Physics of Everyday Phenomena
F is directed out of the screen.
Vector Cross Product
•
•
•
•
Operation symbol 
Another way to multiply two vectors
Product is a vector!
Direction of AB is perpendicular to
both A and B
Cross Product Magnitude
a
q
A  B = ab sin q
A
B
b
Maximum for q = 90°
Zero for q = 0°, 180°
Magnitude Geometrically
a
q
A
B
b
AB = area of parallelogram
Magnetic Force on a Charge
•
•
•
•
•
F = 0 unless charge is moving
F = 0 if velocity is  to field
F = maximum if velocity is  to field
F  0 only if charge crosses B field lines
F = qvB sin(q) in general
• If v or B reverse, direction of F reverses
Group Work
What are the units of magnetic field B?
Cross Product Direction
a
q
A
B
b
• Curl right-hand fingers in
direction of q
• Right-hand thumb points
in direction of crossproduct
• Not commutative
AB = –(BA)
Force Direction
F = qv  B
qv
Source: Griffith, The Physics of Everyday Phenomena
Right-Hand Rule
Origami Right Hand
vectors
fold over
qv
current
Force
creases:
in out
Lorenz
paper square
magnetic
field
Group Question
What is the direction of the force on the
object moving with velocity v through
magnetic field B?
B
A.
D.
B.
E.
C.
F.
+
v
Group Question
What is the magnitude of the force on object
A compared to the magnitude of the force on
object B?
A
B
q
v
B
2q
v
Group Work
A particle with charge q has a velocity
perpendicular to a uniform magnetic field.
What will its subsequent path be?
B
q
v
Force on a Current
• Moving charge q traverses a length L of
wire in time t
• Current I = q/t, speed v = L/t
• Force = qvB = qLB/t = LIB
I
B
Group Work
A current runs through one wire of a pair of
side-by-side wires. What is the direction of
the resulting magnetic field at the location of
the other wire?
I
?
Group CPS Question
Two parallel wires carrying currents in the
same direction
A. attract each other.
B. repel each other.
C. have no effect on each other.
Think of their magnetic fields and charge
movements!
Force between parallel currents
What is
the force
on this
current?
IB
Force between parallel currents
Definition of Ampere
• If two parallel wires are held 1 m apart,
• with currents of 1 A through each wire,
• the attractive force between the wires is
2  10–7 N for each meter of length of the
wires.