Download Introduction to Magnetism - Level 5 Physics

Introduction to Magnetism
Introduction to Magnetism
Level 5 Physics
January 2013
Material adapted from MIT 8.02 course notes
Introduction to Magnetism
Introduction
Everyday Knowledge
What is Magnetism?
What do you already know about magnetism?
Introduction to Magnetism
Introduction
Everyday Knowledge
What is Magnetism?
What do you already know about magnetism?
Perhaps you have played with a magnet before and know that it
has a north pole and a south pole.
Unlike poles attract while like poles repel.
Introduction to Magnetism
Introduction
Everyday Knowledge
Observing “Action at a Distance”
Perhaps you have also noticed that magnets seem to produce a
force that “acts over distance”.
Introduction to Magnetism
Introduction
Everyday Knowledge
Observing “Action at a Distance”
Perhaps you have also noticed that magnets seem to produce a
force that “acts over distance”.
This may seem similar to areas in physics you have already studied:
Introduction to Magnetism
Introduction
Everyday Knowledge
Observing “Action at a Distance”
Perhaps you have also noticed that magnets seem to produce a
force that “acts over distance”.
This may seem similar to areas in physics you have already studied:
GMm
Gravitational force: F~g = − 2 r̂
r
where G = 6.67x10−11 N · m2 /kg 2
ke Qq
Electric force: F~e =
r̂
r2
9
2
where ke = 9.0x10 N · m /C 2
Introduction to Magnetism
Introduction
Everyday Knowledge
Observing “Action at a Distance”
Perhaps you have also noticed that magnets seem to produce a
force that “acts over distance”.
This may seem similar to areas in physics you have already studied:
GMm
Gravitational force: F~g = − 2 r̂
r
where G = 6.67x10−11 N · m2 /kg 2
ke Qq
Electric force: F~e =
r̂
r2
9
2
where ke = 9.0x10 N · m /C 2
Therefore, we might suspect that there exists a magnetic force.
Introduction to Magnetism
Introduction
Field Theory
Revising “Action at a Distance”
The idea behind “action at a distance” is an old theory that a force
between two objects can be transmitted through empty space.
Introduction to Magnetism
Introduction
Field Theory
Revising “Action at a Distance”
The idea behind “action at a distance” is an old theory that a force
between two objects can be transmitted through empty space.
What actually happens is the force is transmitted through stresses
in the intervening spaces until the second object is reached.
Introduction to Magnetism
Introduction
Field Theory
Fields
This is the basis of modern field theory, which was proposed by
Maxwell in 1873. Fields allow us to specify the effect a source will
have on a second agent at any position in space.
Introduction to Magnetism
Introduction
Field Theory
Fields
This is the basis of modern field theory, which was proposed by
Maxwell in 1873. Fields allow us to specify the effect a source will
have on a second agent at any position in space.
Recall the following fields you have already seen:
Introduction to Magnetism
Introduction
Field Theory
Fields
This is the basis of modern field theory, which was proposed by
Maxwell in 1873. Fields allow us to specify the effect a source will
have on a second agent at any position in space.
Recall the following fields you have already seen:
F~g
GM
Gravitational field: ~g =
= − 2 r̂
m
r
~
Fe
ke Q
Electrical field: ~E =
= 2 r̂
q
r
Introduction to Magnetism
Introduction
Field Theory
Fields
This is the basis of modern field theory, which was proposed by
Maxwell in 1873. Fields allow us to specify the effect a source will
have on a second agent at any position in space.
Recall the following fields you have already seen:
F~g
GM
Gravitational field: ~g =
= − 2 r̂
m
r
~e
F
k
Q
e
Electrical field: ~E =
= 2 r̂
q
r
Introduction to Magnetism
Introduction
Field Theory
Fields
This is the basis of modern field theory, which was proposed by
Maxwell in 1873. Fields allow us to specify the effect a source will
have on a second agent at any position in space.
Recall the following fields you have already seen:
F~g
GM
Gravitational field: ~g =
= − 2 r̂
m
r
~e
F
k
Q
e
Electrical field: ~E =
= 2 r̂
q
r
Therefore, we might suspect that there exists a magnetic field.
Introduction to Magnetism
Introduction
Plan
Topics
The magnetic forces caused by magnetic fields that we have
inferred do indeed exist.
Introduction to Magnetism
Introduction
Plan
Topics
The magnetic forces caused by magnetic fields that we have
inferred do indeed exist.
Topics we will address:
Introduction to Magnetism
Introduction
Plan
Topics
The magnetic forces caused by magnetic fields that we have
inferred do indeed exist.
Topics we will address:
Formula for magnetic force
Sources of magnetic fields
Magnetic materials and applications
Introduction to Magnetism
Theory
Point Charge
Experimental Observations
Experimenters have made the following observations about a
~
particle of charge q moving at a velocity ~v in a magnetic field B:
Introduction to Magnetism
Theory
Point Charge
Experimental Observations
Experimenters have made the following observations about a
~
particle of charge q moving at a velocity ~v in a magnetic field B:
1 The magnitude of F~B exerted on the charged particle is
proportional to both v and q
Introduction to Magnetism
Theory
Point Charge
Experimental Observations
Experimenters have made the following observations about a
~
particle of charge q moving at a velocity ~v in a magnetic field B:
1 The magnitude of F~B exerted on the charged particle is
proportional to both v and q
2
~
The magnitude and direction of F~B depends on ~v and B
Introduction to Magnetism
Theory
Point Charge
Experimental Observations
Experimenters have made the following observations about a
~
particle of charge q moving at a velocity ~v in a magnetic field B:
1 The magnitude of F~B exerted on the charged particle is
proportional to both v and q
2
3
~
The magnitude and direction of F~B depends on ~v and B
~ the magnetic force F~B has
When ~v makes an angle θ with B,
~ and magnitude
direction perpendicular to both ~v and B
proportional to sin θ
Introduction to Magnetism
Theory
Point Charge
Experimental Observations
Experimenters have made the following observations about a
~
particle of charge q moving at a velocity ~v in a magnetic field B:
1 The magnitude of F~B exerted on the charged particle is
proportional to both v and q
2
3
4
~
The magnitude and direction of F~B depends on ~v and B
~ the magnetic force F~B has
When ~v makes an angle θ with B,
~ and magnitude
direction perpendicular to both ~v and B
proportional to sin θ
When the sign of q switches, the direction of F~B also switches.
Introduction to Magnetism
Theory
Point Charge
Experimental Observations
Experimenters have made the following observations about a
~
particle of charge q moving at a velocity ~v in a magnetic field B:
1 The magnitude of F~B exerted on the charged particle is
proportional to both v and q
2
3
4
~
The magnitude and direction of F~B depends on ~v and B
~ the magnetic force F~B has
When ~v makes an angle θ with B,
~ and magnitude
direction perpendicular to both ~v and B
proportional to sin θ
When the sign of q switches, the direction of F~B also switches.
What formula for F~B satisfies these criteria?
Introduction to Magnetism
Theory
Point Charge
Review of Special Products
Dot Product
~ and B
~ separated by angle θ
The dot product of two vectors A
produces a scalar:
~ ·B
~ = kAk kBk cos θ
A
Introduction to Magnetism
Theory
Point Charge
Review of Special Products
Dot Product
~ and B
~ separated by angle θ
The dot product of two vectors A
produces a scalar:
~ ·B
~ = kAk kBk cos θ
A
Cross Product
~ and B
~ separated by angle θ
The cross product of two vectors A
produces a vector:
~ ~ A × B = kAk kBk sin θ
with direction given by the right-hand rule
Introduction to Magnetism
Theory
Point Charge
Magnetic Force on Point Charge
Magnetic Force
The magnetic force on a particle of charge q moving at a velocity
~ is given by the formula
~v in a magnetic field B
~
F~B = q~v × B
Introduction to Magnetism
Theory
Current-Carrying Wire
Current
Electric current is simply a collection of moving charged particles.
Thus, a wire carrying an electric current I should experience a
magnetic force as well.
Introduction to Magnetism
Theory
Current-Carrying Wire
Current
Electric current is simply a collection of moving charged particles.
Thus, a wire carrying an electric current I should experience a
magnetic force as well.
Suppose you have a wire of length ` and cross-sectional area A. If
each charged particle has charge q and n is the number of charges
per unit volume, the total charge of the wire is
Qtotal = q(nA`)
Introduction to Magnetism
Theory
Current-Carrying Wire
Current
Electric current is simply a collection of moving charged particles.
Thus, a wire carrying an electric current I should experience a
magnetic force as well.
Suppose you have a wire of length ` and cross-sectional area A. If
each charged particle has charge q and n is the number of charges
per unit volume, the total charge of the wire is
Qtotal = q(nA`)
If the charged particles move at an average drift velocity of v~d , the
current is
I = nqvd A
Introduction to Magnetism
Theory
Current-Carrying Wire
Derivation
We can derive the magnetic force on a wire using Qtotal = q(nA`)
and I = nqvd A.
Introduction to Magnetism
Theory
Current-Carrying Wire
Derivation
We can derive the magnetic force on a wire using Qtotal = q(nA`)
and I = nqvd A.
~
F~B = Qtotal v~d × B
~
= qnA`(v~d × B)
~
= nqvd A(~` × B)
~
= I (~` × B)
where ~` is a length vector with magnitude ` and the same direction
as the current (and v~d )
Introduction to Magnetism
Theory
Current-Carrying Wire
Magnetic Force on Current-Carrying Wire
Magnetic Force
The magnetic force on a wire carrying current I with length vector
~` in a magnetic field B
~ is given by the formula
~
F~B = I ~` × B
Introduction to Magnetism
Theory
Current-Carrying Wire
Closed Loop
~ is
The differential corresponding to F~B = I ~` × B
~
d F~B = I (d~s × B)
where d~s is a small segment of the wire.
Introduction to Magnetism
Theory
Current-Carrying Wire
Closed Loop
~ is
The differential corresponding to F~B = I ~` × B
~
d F~B = I (d~s × B)
where d~s is a small segment of the wire.
If the wire forms a closed loop and the magnetic field is constant,
then the total force on the wire is zero.
H
~ = ~0
F~B = I ( d~s) × B
Introduction to Magnetism
Theory
Units
Tesla
~ is the tesla (T). Its equivalence
The SI unit for a magnetic field B
~
~
can be derived from FB = q~v × B.
Newton
(Coulomb)(meter/second)
N
=1
C · m/s
N
=1
A·m
1 tesla = 1T = 1
Introduction to Magnetism
Theory
Units
Tesla
~ is the tesla (T). Its equivalence
The SI unit for a magnetic field B
~
~
can be derived from FB = q~v × B.
Newton
(Coulomb)(meter/second)
N
=1
C · m/s
N
=1
A·m
1 tesla = 1T = 1
Another common non-SI unit is the gauss (G), where 1T = 104 G .
Introduction to Magnetism
Theory
Units
Tesla
~ is the tesla (T). Its equivalence
The SI unit for a magnetic field B
~
~
can be derived from FB = q~v × B.
Newton
(Coulomb)(meter/second)
N
=1
C · m/s
N
=1
A·m
1 tesla = 1T = 1
Another common non-SI unit is the gauss (G), where 1T = 104 G .
For reference, the magnetic field strength at the Earth’s surface
varies from 0.25 to 0.65 gauss.
Introduction to Magnetism
Questions
Concept Questions
Point Charge Force
Consider a particle of charge q with velocity vector ~v moving in a
~ What is the magnetic force F~B if ~v is parallel to
magnetic field B.
~
B?
~
1 −q~
v×B
2
~0
3
~
q~v × B
Introduction to Magnetism
Questions
Concept Questions
Point Charge Force
Consider a particle of charge q with velocity vector ~v moving in a
~ What is the magnetic force F~B if ~v is parallel to
magnetic field B.
~
B?
~
1 −q~
v×B
2
~0
3
~
q~v × B
Correct Answer: 2
~ is 0, and since the cross product
(The angle between ~v and B
involves sin(0), the magnetic force is ~0.)
Introduction to Magnetism
Questions
Concept Questions
Point Charge Velocity
Consider a particle of charge q with velocity vector ~v moving in a
~ How does ~v change due to F~B if ~v is not parallel
magnetic field B.
~
to B?
1
No change
2
Only magnitude changes
3
Only direction changes
4
Magnitude and direction change
Introduction to Magnetism
Questions
Concept Questions
Point Charge Velocity
Consider a particle of charge q with velocity vector ~v moving in a
~ How does ~v change due to F~B if ~v is not parallel
magnetic field B.
~
to B?
1
No change
2
Only magnitude changes
3
Only direction changes
4
Magnitude and direction change
Correct Answer: 3
(F~B is perpendicular to ~v, so it can only modify the direction.)
Introduction to Magnetism
Questions
Concept Questions
Negative Point Charge
Consider a negative particle with velocity vector ~v moving in a
~ as shown below. What is the direction of the
magnetic field B
resulting magnetic force?
1
Out of the page
2
In the plane of the page
3
Into the page
Introduction to Magnetism
Questions
Concept Questions
Negative Point Charge
Consider a negative particle with velocity vector ~v moving in a
~ as shown below. What is the direction of the
magnetic field B
resulting magnetic force?
1
Out of the page
2
In the plane of the page
3
Into the page
Correct Answer: 1
(The right-hand rule produces the correct magnetic force for a
positive charge. Reverse the direction given by the right-hand rule
for a negative charge.)
Introduction to Magnetism
Questions
Concept Questions
Point Charge Work
In the same situation as the previous problem, F~B will do what
amount of work on the particle over time?
1
Negative
2
Zero
3
Postive
Introduction to Magnetism
Questions
Concept Questions
Point Charge Work
In the same situation as the previous problem, F~B will do what
amount of work on the particle over time?
1
Negative
2
Zero
3
Postive
Correct Answer: 2
~ · ~vdt = 0.)
(dW = F~B · d~s = q(~v × B)
Introduction to Magnetism
Questions
Concept Questions
Force on Wire
Suppose a positive current is traveling downward through a wire.
A portion of the wire runs through a uniform magnetic field
pointing out of the page. Which behavior of the wire would you
expect to see?
1
2
3
Introduction to Magnetism
Questions
Concept Questions
Force on Wire
Suppose a positive current is traveling downward through a wire.
A portion of the wire runs through a uniform magnetic field
pointing out of the page. Which behavior of the wire would you
expect to see?
1
2
Correct Answer: 2
(Apply the right hand rule.)
3
Introduction to Magnetism
Questions
Concept Questions
Closed Loop
A semi-circular loop with radius R carrying a current I is placed in
a uniform magnetic field. What is the net force on only the curved
portion of the loop?
1
2RIB, into the page
2
0
3
2RIB, out of the page
Introduction to Magnetism
Questions
Concept Questions
Closed Loop
A semi-circular loop with radius R carrying a current I is placed in
a uniform magnetic field. What is the net force on only the curved
portion of the loop?
1
2RIB, into the page
2
0
3
2RIB, out of the page
Correct Answer: 1
(If the wire forms a closed loop and the magnetic field is constant,
then the total force on the wire is zero.)