Lorentz Force Law and Right Hand Rules
• We can use our magnet to move (or change the velocity) of bits of
metal
• If we apply a current (by connecting a battery) we can create an
electromagnet that did the same thing.
Recall Newton's law that an object will remain at rest unless acted on
by an outside force, so the magnet and the electrical current must
be generating some kind of force.
Lorentz Force
• Lorentz force is the force experienced by a charge moving in
an electromagnetic field.
• Lorentz force is determined by the formula F = qv x B
– q is the magnitude of the charge(Coulomb)
– v is the velocity (m/s)
The x represents a process called
– B is the magnetic field density. (Tesla)
is perpendicular to B and both are
a vector cross-product in which qv
perpendicular to F.
• Lorentz force is perpendicular to both velocity and magnetic
field. The right hand rule is applied when determining Lorentz
force.
The three quantities I,B and F and all at right angles to each
other. This is called "orthogonal".
I
B
F
Begin by lining your thumb up with the current. Then rotate your hand to line your finger with the magnetic
field. The direction of your palm is the direction of the force on the wire.
http://www.youtube.com/watch?v=_X8jKqZVwoI
Representing Vectors in Three Dimensions
Motion comes in three pairs of directions:
Left
Up
up
Right
in
Down
left
Into page
Out of page
right
out
down
Conventions for Flowing Current or Electric Charge
Electrons, electron current flow or anything
negative
left hand
Protons, conventional current flow or anything
positive
right hand.
We will use conventional current p+ and right hand
rules.
Marking Up your Hand
Draw a I for current on your thumb
Draw an B for magnetic field on your index
finger
Draw a F for force on your palm
B
F
I
The first set of rules is for a moving charge in an EXTERNAL
magnetic field (We ignore the field generated by the moving
electrons).
The last set of rules is for the magnetic field generated BY the
electrons moving around a wire itself.
http://www.youtube.com/watch?v=LK7hv4LX3ys&feature=related&safe=active
Force on a wire resulting from a magnetic field
B
F
I
Begin by lining your thumb up with the current. Then rotate your hand to
line your finger with the
magnetic field. The direction your palm is the direction of the force on the
wire.
You can start with any of the other fingers, depending on what you are given
in the question, by lining up
one finger and rotating the second until it lines up properly. The palm will be
pointed in the correct
direction.
Examples: Movement in an EXTERNAL Magnetic Field
Find the direction of the current, the magnetic field and the Lorentz
Force.
N
S
p+ = out
_____
of page
B = down
______
- from N pole to S pole so B is
down - Align my thumb with current,
F = Right
______
rotate my fingers to align with B (down)
and my palm faces to the right
Assume the current in the wire is conventional flow (+ve).
Examples
Find the direction of the current, the magnetic field and the Lorentz
Force.
p+ = _____
out of page
up -from N to S so B is up
B = ______
F = ______
Left -Align my thumb with current, rotate
S
N
my fingers to align with B (up) and my
palm faces to the left
Assume the current in the wire is conventional flow (+ve).
Examples
Find the direction of the current, the magnetic field and the Lorentz
Force.
..........
..........
p+ . . . . . . . . . .
..........
..........
..........
p+ = _____
to the right
B = ______
out of page
F = ______
Down -Align my thumb with current,
rotate my fingers to align with B (out of
page) and my palm faces down
Assume the current in the wire is conventional flow (+ve).
"Wire-Grasp" Rule for the Magnetic Field Generated BY the Wire
Recall that the magnetic field lines around a wire form circles around
the wire.
We can use a compass to determine the direction of the Magnetic field
in the wire or we can use the "Wire-wrap Rule"
Using the "Wire-Grasp" Rule for the Magnetic Field Generated BY the
Wire
• Line your thumb up with the direction of the conventional current
flowing in the wire (+ve).
• Imagine you are curling your fingers around the wire.
• Your fingers point in the direction the magnetic field is pointing. (Up
on one side of the wire and down on the other.
Don't use this rule if there is an external applied
field.
For conventional current
Example: Consider the following current carrying wires. Draw the
magnetic fields generated by the wires.
p+
p+
a) Straight wire
b) Current in a loop of wire
Solenoids
• A solenoid is a long coil of thin wire, which when wrapped around
a piece of metal, produces a magnetic field when an electric
current is passed through it.
• Solenoids are important because they can create controlled
magnetic fields and can be used as electromagnets.
Coils of wire
Polarity of a solenoid
Method 1:
To find the polarity of a solenoid point your fingers in the direction of
the conventional current as it enters the solenoid. Your thumb will
point in the direction of N-pole of the solenoid.
Method 2:
To find the polarity of a solenoid, we use the clock rule. Remember the
mnemonic.....
aNticlockwise = North Pole
clockwiSe = South Pole
Face the end of the solenoid. If the direction of current is anticlockwise
from your end, it is the North Pole, else, if clockwise it is the south
pole
Example
p+
current is moving
clockwise => South
pole
Polarity of a Magnet
Curl your fingers around the wire with your thumb
pointing in the direction of the conventional current
(flow of +ve charge). Your thumb points to the
North end of the solenoid.
Left hand Rules-Use when there is a negative charge flow
Forces on a Current
Carrying Wire
Lorentz Force on a Wire
For a single charge the force it will experience in an external magnetic
field is given by:
F = qv x B
Only that portion of the velocity vector that is perpendicular to the
magnetic field will contribute to the force.
The implications of this expression include:
•
The force is perpendicular to both the velocity v of the charge q
• and the magnetic field B.
•
The magnitude of the force is F = qvB sinθ where θ is the angle <
• 180 degrees between the velocity and the magnetic field.
•
This implies that the magnetic force on a stationary charge or a
• charge moving parallel to the magnetic field is zero.
•
The direction of the force is given by the right hand rule. The force
• relationship above is in the form of a vector product.
Magnetic Force on a Current Carrying Wire
• If a wire carrying a current is placed in a magnetic field each of the
charges moving in the wire will experience a magnetic force along
the length of the wire that is in the field.
. . . . . . . . . B is out of the page
. . . . L. . . . .
.
current .
. . . . . . . . .F
.........
.
.
.........
.........
L = .the length of wire in the magnetic field
.
I = conventional current (+ve)
Finding the Force Equation
F = q v B sinθ
= q (L/t)B sinθ
= (q/t)L B sinθ
= ILBsinθ
F = BILsinθ
F = BILsinθ
The magnitude of the force is proportional to the current I, the
magnetic field, B and the length of the wire that is in the magnetic
field. θ is the angle between the current and the direction of the
magnetic field.
Use the RHR to find the direction of the Force.
Deriving units for B
F= ILBsinθ
B = F/IL
= N/A m
A = 1C/s
Example 1
A power line carries a current of 1.54 x 103 A in Greenland at a spot where
the magnetic field is 5.60 x 10-5 T. The power line makes an angle of 36o
to the field. What is the magnitude of the Force on a 220 m length of the
wire?
Example 2:
A 10.0 cm wire carries a current of 5.0 A. The wire is at right angles to
the uniform magnetic field. The force on the wire is 2.0 N. What is the
magnitude of the magnetic field?
Example 3:
In March 1967, a 1000T magnetic field was obtained in a lab for a
fraction of a second. (The maximum sustained field is about 45T.) If a
25 cm wire is perpendicular to a 1 x 103 T magnetic field and the
magnetic force on the wire is 1.6 x 102 N, what is the current?
Why does the wire move?
When a current-carrying conductor is placed in a magnetic field, the
interaction between the two magnetic fields will produce a net force on the
conductor.
The interaction of the two magnetic fields (the magnetic field of the currentcarrying wire and the magnetic field of the permanent magnet) produces a
resultant that is the vector sum of the two fields.
This sum produces a non-uniform field that moves the wire from the
stronger field to the weaker field
Strength of the Force
The strength of the force can be increased by:
•
•
>Increase the current
>Using a stronger magnet
Assignment
Read/Study pages 19-24
Complete
25 and 26
page 29
page 34
and q.1-17 on page 17