Transcript Direction of Magnetic Force

A Brief Recap
Charged particles in motion create
magnetic fields around themselves.
We can use Right-Hand Rule #1 to determine
the direction of a magnetic field produced by
one or more charged particles in motion.
The Principle of Superposition applies to
B fields just as it did to E fields.
Whiteboard Warmup
Sketch the magnetic field of a loop of wire from a
cross-sectional view. (Imagine a donut cut in half
and looked at from the side)
I
I
Use RHR #1 for each section of the loop, and then
use the Principle of Superposition!
Superposition Whiteboard
Two wires carrying equal currents are crossed, as shown above.
Determine the magnetic field in each of the labeled regions.
B=0T
B=0T
B Field of a Current-Carrying Wire
r
m0 I
B=
2p r
Directly proportional
to the current
through the wire
Drops off hyperbolically with
radial distance from wire
μ0 is a constant called the permeability of free space
μ0 = 1.3 x 10-6 T*m/A
Current Events
Two parallel wires are each carrying a current of 0.8 Ampères
upward, as shown below. Calculate the magnitude and direction
of the magnetic field at points A, B and C shown below.
10 cm
μ0 = 1.3 x 10-6 T*m/A
10 cm
6 cm 4 cm
10 cm
10 cm
6 cm 4 cm
m0 I
B=
2p r
Vector superposition in
the third dimension!
BA = 2.2 x 10-6 T out of the page
BB = 0 T
BC = 3.1 x 10-6 T out of the page
Magnetic Force
Just as charged particles in motion create
magnetic fields, charged particles in motion
are the only thing that can feel a force
exerted by a magnetic field.
Moving charged particles create B fields.
Other moving charged particles in these
B fields can feel a force from the field.
Magnetism: It’s All Perpendicular
A charged particle moving in a B field will only feel a
magnetic force if some component of its velocity is
perpendicular to the B field.
B
v
v
v
Motion perpendicular
to B field:
Maximum magnetic
force
Some component of
motion perpendicular
to B field:
Some magnetic force
Motion parallel or
antiparallel to field:
Zero magnetic force
Strength of the Magnetic Force
B
θ
v
q
FB = qvBsinq
•
•
•
•
Depends on four things
Magnitude of charge
Speed of particle
Strength of B field
How much of the
velocity is perpendicular
to the field
Angle between v and B
If θ = 0° or 180°, FB =
0N
If θ = 90°, FB = qvB
Direction of Magnetic Force
The magnetic force felt by a particle will be
perpendicular to the particle’s velocity, and
also perpendicular to the magnetic field.
To model this accurately, we need
to use another right-hand rule!
Right Hand Rule #2
2. Then, while keeping your
thumb in that direction, twist
your right hand so that your
fingers align with the B field
3. Your palm will
now point in the
direction of the
magnetic force!
1. First, align your thumb with
the direction of the current
(flow of positive charge)
RHR #2: It’s fun, 3-D and easy to remember!
Thumb: Current
Fingers: Field
Palm: Push
Warning! Make sure that your
thumb stays aligned with the
current while you are lining up
your fingers with the B field.
WB: What is the direction of FB?
FB
FB
FB
FB
Whiteboard: Which way is FB?
a)
b)
v
I
v
a)B field is into page.
Force is upward.
b) B field is upward.
Force is zero.
Negative Charges in B-Fields
The force will be in the opposite direction
than if the particle were positive.
1. Point your thumb in the
direction of the negative
particle’s motion
2. Turn your hand to align your
fingers with the B-field.
3. The force felt by the negative
charge will point away from
the back of your hand!
Which way will the electron feel a
magnetic force?
I
v
Solution
B
v
FB
For Tomorrow’s Quiz
Know how to:
1. Determine the magnitude and direction of a
magnetic field formed by a current-carrying
wire.
2. Determine the direction of the magnetic field
formed by a magnet or loop of current.
3. Determine the magnitude and direction of the
magnetic force felt by a positive or negatively
charged particle in a magnetic field.