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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.
Lorentz Force Law:
The magnitude of the magnetic force
on a moving, charged particle is
F = qvB sin q
q = charge [C]
V = velocity [m/s]
B = magnetic field [T]
q = the angle between the
charge’s velocity and the
magnetic field
The unit of magnetic field, B, is Tesla
(T) in honor of Nikola Tesla
1 T = 1 N·s/(C·m)
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 #1
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.
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 Fields can be used to generate
electricity!
If a conductor is moved through a magnetic field, the charges
are pushed by the magnetic force. This leads to an
accumulation of charge -- or potential difference -- on one
side of the conductor.
This process is called electromagnetic induction. If
connected to a circuit, this induced potential difference (emf!)
will cause a current to flow.
Electric induction underlies MANY devices including
• electric generators
• electric motors
• transformers
• Etc, etc, etc.
Magnetic Fields can be used to generate
electricity!
In this class, we will just have to solve for one induction
scenario:
A conductor moved
perpendicularly through a
stationary magnetic field
In this case,
V = lvB
Where
V = induced potential difference (emf)
l = length of the conductor
v = velocity of the conductor
B = magnetic field strength
Magnetic Fields can be used to generate
electricity!
Example:
A potential difference of 9 volts is induced across a straight
wire of 0.5 m long as it is moved at constant speed of 4 m/s
perpendicularly through a magnetic field. What is the
strength of the magnetic field?
V = lvB
B=
𝑉
𝑙𝑣
B=
9𝑉
0.5 𝑚 4 𝑚/𝑠
= 4.5 T
Electricity can be used to generate magnetic
fields!
Example: Solenoids.
A solenoid is a coil of currentcarrying wire. As the current goes
through the coil it creates a strong,
uniform magnetic field through the
center of the coil.
More current and more coils =
stronger magnetic field
▪ If we place an iron core inside the
solenoid we have an electromagnet.
▪The ferrous core enhances the
strength of the B-field
▪ Used to create a strong, uniform
magnetic field
RHR for Solenoids!
Grasp the solenoid with your right hand in such a way that
your fingers curl in the direction of the current.
Your extended thumb points in the direction of north pole.
PRACTICE: In the solenoid shown
label the north and south poles.
I
I
PRACTICE: The north and south
poles are labeled in the solenoid.
Sketch in the current, both
entering and leaving the solenoid.