Download Strength of Magnetic Force

Magnetic Force
Strength of Magnetic Force
A charged particle moving in a magnetic field experiences a
force that is perpendicular to BOTH the particle’s velocity
and to the magnetic field itself.
Strength of Magnetic Force
A charged particle moving in a magnetic field experiences a
force that is perpendicular to BOTH the particle’s velocity
and to the magnetic field itself.
Lorentz Force Law:
The magnitude of the magnetic force
on a moving, charged particle is
F = qvB sin q
(q is the angle between the
charge’s velocity and the
magnetic field)
F = qvB sin q
Sin 0, 180 = 0 If a charge has velocity in the same (or opposite)
direction of the magnetic field, it experiences no force!
Sin 90 = 1 A charge that has velocity perpendicular to the
magnetic field experiences the greatest force!
Question?
The three charges below have equal charge and speed,
but are traveling in different directions in a uniform
magnetic field.
Which particle experiences the greatest magnetic force?
1
2
3
3
2
1
Same
B
F = q v B sin q
The direction of the magnetic force is
given by the Right-Hand Rule
F
► Point fingers in v (or current I)
direction
positive
charge
B
► Curl fingers as if rotating
vector v (current I) into B.
q
v
charge q moving with
velocity v in the mag.
field B
F
negative
charge
► Thumb is in the direction of the
force.
● For negative charge force is
in the opposite direction
F is perpendicular to the
plane of v and B
Convention for magnetic field
direction:
x x x x x x x INTO Page
•••••••••••••
Right Hand Rule
Practice
OUT of Page
A proton enters a magnetic
field, as shown. Which way
will the electron turn?
1.
2.
3.
4.
Up
Down
Out of page
Into page
Convention for magnetic field
direction:
x x x x x x x INTO Page
•••••••••••••
Right Hand Rule
Practice
OUT of Page
A proton enters a magnetic
field, as shown. Which way
will the electron turn?
1.
2.
3.
4.
Up
Down
Out of page
Into page
Put your fingers in
the direction of the
velocity and curl out
of the page … your
thumb points up
Convention for magnetic field
direction:
x x x x x x x INTO Page
•••••••••••••
Right Hand Rule
Practice
OUT of Page
An electron enters a magnetic
field, as shown. Which way
will the electron turn?
1.
2.
3.
4.
Up
Down
Out of page
Into page
Convention for magnetic field
direction:
x x x x x x x INTO Page
•••••••••••••
Right Hand Rule
Practice
OUT of Page
An electron enters a magnetic
field, as shown. Which way
will the electron turn?
1.
2.
3.
4.
Up
Down
Out of page
Into page
Remember to flip
the direction of the
force for negative
charges
Convention for magnetic field
direction:
x x x x x x x INTO Page
•••••••••••••
Right Hand Rule
Practice
OUT of Page
In which direction will wire
segment B be pushed?
1.
2.
3.
4.
5.
Up
Down
Out of page
Into page
No force exists
Convention for magnetic field
direction:
x x x x x x x INTO Page
•••••••••••••
Right Hand Rule
Practice
OUT of Page
In which direction will wire
segment B be pushed?
1.
2.
3.
4.
5.
Up
Down
Out of page
Into page
No force exists
Convention for magnetic field
direction:
x x x x x x x INTO Page
•••••••••••••
Right Hand Rule
Practice
OUT of Page
In which direction will wire
segment C be pushed?
1.
2.
3.
4.
5.
Up
Down
Out of page
Into page
No force exists
Convention for magnetic field
direction:
x x x x x x x INTO Page
•••••••••••••
Right Hand Rule
Practice
OUT of Page
In which direction will wire
segment C be pushed?
1.
2.
3.
4.
5.
Up
Down
Out of page
Into page
No force exists
V and B are
in the same
direction; no
force exists.
Magnitude of the magnetic field
We define the magnitude of the magnetic field by measuring
the force on a moving charge
:
F
B
qv sin q
B
q
v
The SI unit of magnetic field is the Tesla (T), named after
Nikola Tesla, a Croatian physicist.
1 T = 1 N·s/(C·m)
N
Ns

m Cm
C
s
Magnetic Field & Magnetic Force Problems
We do:
What is the minimum magnetic field necessary to exert a 5.4
X 10-15 N force on an electron moving at 2.1 X 107 m/s?
Magnetic Field & Magnetic Force Problems
We do:
What is the minimum magnetic field necessary to exert a 5.4
X 10-15 N force on an electron moving at 2.1 X 107 m/s?
B = F / qvsinθ
B will be at a minimum when sin θ = 1
B = F / qv = 5.4X10-15N / (1.6 X 10-19 C X 2.1 X 107 m/s)
B = 1.61 X 10-3 T
Magnetic Field & Magnetic Force Problems
You do:
What is the magnetic field necessary to exert a 5.4 X 10-15 N
force on an electron moving at 2.1 X 107 m/s if the magnetic
field is at 45 degrees from the electron’s velocity?
Magnetic Field & Magnetic Force Problems
You do:
What is the magnetic field necessary to exert a 5.4 X 10-15 N
force on an electron moving at 2.1 X 107 m/s if the magnetic
field is at 45 degrees from the electron’s velocity?
B = F / qvsinθ = 5.4X10-15N / (1.6 X 10-19 C X 2.1 X 107 m/s X
sin 45)
B = 2.3 X 10-3 T.
Magnetic Field & Magnetic Force Problems
We do and You do
What is the magnitude of the magnetic force on a proton
moving at 2.5 X 105 m/s in a magnetic field of 0.5 T …
(a) …if the velocity and magnetic field are at right angles?
(b) … if the velocity and magnetic field are at 30°?
(c) … if the velocity is parallel to a magnetic field?
Magnetic Field & Magnetic Force Problems
We do and You do
What is the magnitude of the magnetic force on a proton
moving at 2.5 X 105 m/s in a magnetic field of 0.5 T …
(a) …if the velocity and magnetic field are at right angles?
(b) … if the velocity and magnetic field are at 30°?
(c) … if the velocity is parallel to a magnetic field?
F = qvBsinθ , so
(a) when θ = 90°, F = (1.6 X 10-19 C)(2.5 X 105 m/s)(0.5 T) =
2.0 X 10-14 N,
(b) F = (2.0 X 10-14 N) sin 30° = 1.0 X 10-14 N, and
(c) F = qvB sin 0° = 0.
Comparison of Electric and Magnetic Forces
Using your notes, and working in small groups (3 or less),
compare the electric and magnetic forces in terms of:
•
•
•
•
Magnitude
Direction
Work done
Effect on charged particles
Comparison of Electric and Magnetic Forces
The electric force:
Felec = Eq
The magnetic force:
Fmag = qvB sin q
 is always parallel to the direction  is always perpendicular to the direction of the
of the electric field.
magnetic field
 acts on a charged particle only when the
 acts on a charged particle
independent of the particle’s
particle is in motion (F=0 if v=0), and only
velocity
if v and B do not point in the same or opposite
direction (sin 00 = sin 1800 = 0).
 does work when moving charge:  Force is perpendicular to motion so the work
done by magnetic force is zero.
The work, W = Fel d cosθ1, is
W = Fmagd cosq1  0 (cos 900 = 0).
converted into kinetic / thermal energy.
Change in kinetic energy of the charge is 0
The electric field accelerates
charged particles.
In the presence of magnetic field, the moving
charged particle is deflected (dotted lines)