Magnetism

1
Magnetism
I
2
Music

• Who is the Artist?
• Peter Tosh
• Bob Marley
• Toots and the Maytals
• Jimmy Cliff
• Eric Clapton

3
Magnetic Observations

• Bar Magnets
• Compass Needles
• Magnetic Charge?

N S
N S
S N
N S
N S
cut in half
N S
N S
N S
N S
4
Magnetic Observations

• Compass needle deflected by electric current

I

• Magnetic fields created by electric currents
• Magnetic fields exert forces on electric currents
  (charges in motion)

I
F
I
F
F
I
I
F
5
Magnetism Moving Charges

• All observations are explained by two simple
  equations

Today
Next Week
6
Magnetic Force
y
x
F
B
v
z
7
Remembering Directions The Right Hand Rule
y
x
F
B
v
z
8
Some not-so-good pictures claiming to illustrate
the RHR
9
Cross Product Recap (from Physics 211)
B

• Cross Product different from Dot Product
• A?B is a scalar AXB is a vector
• A?B proportional to the component of B parallel
  to A
• AXB proportional to the component of B
  perpendicular to A
• Definition of AXB
• Magnitude ABsinq
• Direction perpendicular to plane defined by A
  and B with sense given by right-hand-rule
• w/ hand flat, point fingers of right hand in
  direction of A
• curl fingers in direction of B
• thumb straight points in direction of AXB

q
A
v
F qv X B
q
q
B
F points into the screen
10
Motion of Charge q in Uniform B Field

• Force is perpendicular to v
• Speed does not change
• Uniform Circular Motion

• Solve for R

R
Uniform B into page
11
Preflight
Three points are arranged in a uniform magnetic
field. The B field points into the screen.
1) A positively charged particle is located at
point A and is stationary. The direction of the
magnetic force on the particle is
a) right b) left c) into
the screen d) out of the screen
e) zero
12
Preflight
3) The positive charge moves from point A toward
C. The direction of the magnetic force on the
particle is
a) up and right b) up and left
c) down and right d) down and left
13
Preflight
The drawing below shows the top view of two
interconnected chambers. Each chamber has a
unique magnetic field. A positively charged
particle is fired into chamber 1, and observed to
follow the dashed path shown in the figure.
5) What is the direction of the magnetic field in
chamber 1?
a) Up b) Down
c) Left d) Right
e) Into page f) Out of
page
14
Preflight
6) What is the direction of the magnetic field in
chamber 2?
a) Up b) Down
c) Left d) Right
e) Into page f) Out of
page
15
Preflight
8) Compare the magnitude of the magnetic field in
chamber 1 to the magnitude of the magnetic field
in chamber 2.
a) B1 B2 b) B1 B2 c) B1
16
Calculation
exits here
A particle of charge q and mass m is accelerated
from rest by an electric field E through a
distance d and enters and exits a region
containing a constant magnetic field B at the
points shown. Assume q,m,E,d, and x0 are
known. What is B?
x0/2
R1
X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X
q,m
x0
R3
d
enters here
V
B
B

• Absolutely ! We need to use the definitions of V
  and E and either conservation of energy or
  Newtons Laws to understand the motion of the
  particle before it enters the B field.
• We need to use the Lorentz Force Law (and
  Newtons Laws) to determine what happens in the
  magnetic field.

17
Calculation
exits here
A particle of charge q and mass m is accelerated
from rest by an electric field E through a
distance d and enters and exits a region
containing a constant magnetic field B at the
points shown. Assume q,m,E,d, and x0 are
known. What is B?
x0/2
R1
X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X
q,m
x0
R3
d
enters here
V
B
B

• Strategic Analysis
• Calculate v, the velocity of the particle as it
  enters the magnetic field
• Use Lorentz Force equation to determine the path
  in the field as a function of B
• Apply the entrance-exit information to determine
  B

Lets Do It !!
18
Calculation
exits here
A particle of charge q and mass m is accelerated
from rest by an electric field E through a
distance d and enters and exits a region
containing a constant magnetic field B at the
points shown. Assume q,m,E,d, and x0 are
known. What is B?
x0/2
R1
X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X
q,m
x0
R3
d
enters here
V
B
B

• Why??
• Conservation of Energy
• Initial Energy U qV qEd
• Final Energy KE ½ mv02

• Newtons Laws
• a F/m qE/m
• v02 2ad

19
Calculation
exits here
A particle of charge q and mass m is accelerated
from rest by an electric field E through a
distance d and enters and exits a region
containing a constant magnetic field B at the
points shown. Assume q,m,E,d, and x0 are
known. What is B?
x0/2
R1
X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X
q,m
x0
R3
d
enters here
V
B
B

• Why??
• Path is circle !
• Force is perpendicular to the velocity
• Force produces centripetal acceleration
• Particle moves with uniform circular motion

20
Calculation
exits here
A particle of charge q and mass m is accelerated
from rest by an electric field E through a
distance d and enters and exits a region
containing a constant magnetic field B at the
points shown. Assume q,m,E,d, and x0 are
known. What is B?
x0/2
R1
X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X
q,m
x0
R3
d
enters here
V
B
B

• Why??

21
Calculation
exits here
A particle of charge q and mass m is accelerated
from rest by an electric field E through a
distance d and enters and exits a region
containing a constant magnetic field B at the
points shown. Assume q,m,E,d, and x0 are
known. What is B?
x0/2
R1
X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X
q,m
x0
R3
d
enters here
V
B
B

• Why??

22
Follow-Up
exits here
A particle of charge q and mass m is accelerated
from rest by an electric field E through a
distance d and enters and exits a region
containing a constant magnetic field B at the
points shown. Assume q,m,E,d, and x0 are
known. What is B?
x0/2
R1
X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X
q,m
x0
R3
d
enters here
V
B
B

• Suppose the charge of the particle is doubled (Q
  2q),while keeping the mass constant. How does
  the path of the particle change?

DONE
MORE
23
Follow-Up
exits here
A particle of charge q and mass m is accelerated
from rest by an electric field E through a
distance d and enters and exits a region
containing a constant magnetic field B at the
points shown. Assume q,m,E,d, and x0 are
known. What is B?
x0/2
R1
X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X
q,m
x0
R3
d
enters here
V
B
B

• Suppose the charge of the particle is doubled (Q
  2q),while keeping the mass constant. How does
  the path of the particle change?
• I expected no slam dunk.. Lets talk about this
  one some more.

• Why??

24
Follow-Up
exits here
A particle of charge q and mass m is accelerated
from rest by an electric field E through a
distance d and enters and exits a region
containing a constant magnetic field B at the
points shown. Assume q,m,E,d, and x0 are
known. What is B?
x0/2
R1
X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X
q,m
x0
R3
d
enters here
V
B
B

• Suppose the charge of the particle is doubled (Q
  2q),while keeping the mass constant. How does
  the path of the particle change?

• Why??

25
Follow-Up
exits here
A particle of charge q and mass m is accelerated
from rest by an electric field E through a
distance d and enters and exits a region
containing a constant magnetic field B at the
points shown. Assume q,m,E,d, and x0 are
known. What is B?
x0/2
R1
X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X
q,m
x0
R3
d
enters here
V
B
B

• Suppose the charge of the particle is doubled (Q
  2q),while keeping the mass constant. How does
  the path of the particle change?

• Why??

26
Follow-Up
exits here
A particle of charge q and mass m is accelerated
from rest by an electric field E through a
distance d and enters and exits a region
containing a constant magnetic field B at the
points shown. Assume q,m,E,d, and x0 are
known. What is B?
x0/2
R1
X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X
q,m
x0
R3
d
enters here
V
B
B

• Suppose the charge of the particle is doubled (Q
  2q),while keeping the mass constant. How does
  the path of the particle change?

(A) (B)
(C)
27
Challenge
I1
I3
In this circuit, assume V, C, and Ri are known. C
initially uncharged and then switch S is closed.
S
R1
R2
R3
C
V
What is tc, the charging time constant?
I2

• Strategy
• Write down KVR and KCR for the circuit when S is
  closed
• 2 loop equations and 1 node equation

• Use I2 dQ2/dt to obtain one equation that looks
  like simple charging RC circuit ( (Q/C)
  R(dQ/dt) V 0 )

• Make correspondence R ?, then t RC

C