Download Chapter 27 – Introduction to Magnetic Fields – Review – Electric

Chapter 27 – Introduction to Magnetic Fields –
Review – Electric Fields
1. A charge (or charges) produce an Electric Field
in the space around it.
2. Another charge responds to this field
(experiences a force)
What is coming up for Magnetic Fields
1. A MOVING charge (or charges) produce an Magnetic Field
in the space around it.
2. Another MOVING charge responds to this field
(experiences a force)
Some Simple Phenomenology –
First Guess – Magnetic Forces are just like Electric Forces
Just Replace + & - with N & S
This is an extremely good idea that is, unfortunately
WRONG
The Basic Problem is that there are no “Free” N & S poles.
Experiments show that there is a fundamental relationship
between Magnetic Fields and Electric Currents
Oersted’s Experiment
Place a compass near a wire
Compass deflects when an electric
current flows in the wire
N
Motion of a charged particle in a Magnetic Field
1. A moving charge or a electric current produces a magnetic field in
the surrounding space (It also produces an electric field)
2. The magnetic field exerts a force on any other moving charge or
current that is in the field.
Strategy:
We will begin with a discussion of the force
on a moving charge (part 2.)
Then we will discuss how a moving charge
makes the field (part 1.)
Some examples of the force on a moving charge in a magnetic field
observation #1- The magnetic force is always perpendicular to the
magnetic field
observation #2- The magnetic force is always perpendicular to the
particle velocity
The “Vector” or “Cross Product”
v r r
If C = A × B then the magnitude
r of
where θ is the angle between A and
is given by the “Right Hand Rule”:
r r
v
C
r = A B sin θ ,
r
B . The direction of C
Advice on using the Right Hand Rule:
1) First determine the plane that contains A and B. The cross product will
point perpendicular to that plane. There are only two choices.
2) Use the Right Hand
r Ruler to rpick which choice is correct.
3) If you are using F = qv × B , Remember that a negative charge will reverse
the direction of the cross product!
r
r r
F = qv × B
F = q vB⊥
Units of Magnetic Field:
1 Tesla = 1 T = 1 Newton/(Ampere·meter)
Motion of Charged Particles in Magnetic and Electric Fields
r r r
v
F = q( E + v × B )
EM force – “Lorentz” Force
+
v
r
d2 r
F = ma = m 2 r
dt
Newton’s 2nd Law
r r
d r r r
d2 r
q[ E ( r ) + r × B( r )] = m 2 r
dt
dt
r
r (t )
Differential equation
Solution = “Equation of Motion”
For constant force there are two important simple cases:
v
r r r
r
Uniform linear acceleration v = v0 + at
F is parallel to v
v
r
F is perpendicular to v
Uniform circular motion
Uniform Circular Motion (see Y & F Chapter 3)
Similar triangles gives
Average acceleration
r
∆v ∆s
=
v1
R
r v1
∆v = ∆s
R
r
∆v v1 ∆s
=
R ∆t
∆t
r
∆v v1
r
∆s
a = lim ∆t →0
= lim ∆t →0
R
∆t
∆t
r v2
a =
R
Uniform Circular Motion implies a acceleration
that is always directed towards the center of
the circle.
r
Amplitude of acceleration is constant:
r mv 2
F = ma =
R
Direction of acceleration changes with time
Angular Velocity (see Y& F chapter 9)
Uniform Circular Motion is described by an “Angular Velocity”
ds
Since s = rθ and v =
dt
v = rω
v2
a=
= rω 2
r
v2
F = m = mrω 2
r
ω≡
Angular Velocity (radians/s)
Frequency
ω
f =
2π
cycles/s=Hertz
Period
1
T=
f
seconds
dθ
ω=
dt
Angular Velocity as a vector (see Y& F chapter 9)
┴
Right Hand Rule Gives Sense of Rotation
Given by Torque
End of Chapter 27
You are responsible for the material covered in T&F Sections 27.1 -27.8
You are expected to:
•
Understand the following terms:
magnetic field, magnetic force, uniform circular motion, angular velocity, angular
acceleration, torque, magnetic dipole moment
•
Be able to calculate the force on a moving charge in a uniform magnetic field, be able to calculate
the force on a current carrying conductor, be able to calculate the torque on a loop of wire.
Recommended F&Y Exercises chapter 27:
33,39,41,45