Physics
ys cs 132:
3 Lecture
ectu e 20
0
Elements of Physics II
A
Agenda
d for
f T
Today
d


Forces on currents
 Currents are moving charges
 Torque on current loop
 Torque on rotated loop
Currents create B-fields
 Adding magnetic fields
 Force between wires
Physics 201: Lecture 1, Pg 1
Force on charged particle by B-field

A charged particle will feel a force when it’s
it s in a
B-field if:
 The charge is moving
 Velocity of charge is not completely parallel to
the B-field
B field
B-field
Charge
velocity
No Force
Physics 201: Lecture 1, Pg 2
Force on charged particle by B-field

A charged particle will feel a force when it’s
it s in a
B-field if:
 The charge is moving
 Velocity of charge is not completely parallel to
the B-field
Charge
velocity
B field
B-field
There is a Force
Physics 201: Lecture 1, Pg 3
Direction of Force on charged
particle by B-field


•
Magnitude of force:
 F = qvBsin
The direction of the force is perpendicular to both
the velocity vector and the B
B-field
field vector
Velocity and B-field make a plane, force goes through this
plane.
p
Charge
velocity
B-field
Force is perpendicular to screen!
Physics 201: Lecture 1, Pg 4
Right hand rule


The direction of the force can be found with the
right hand rule
Thumb in direction of velocity, fingers in direction
off B-field,
B fi ld palm
l points
i
where
h
fforce goes
Charge
velocity

B-field
Force goes into page!
Physics 201: Lecture 1, Pg 5
Flat Right Hand Rule

To find the direction of the
force felt by a charged
particle moving in a
magnetic-field
ti fi ld

Thumb = velocity
Fingers = B-field.
Palm = force


 If charge is negative
force is opposite!
Physics 201: Lecture 1, Pg 6
Clicker Question 1:
A proton is shot straight at the center of a long, straight
wire carrying current into the screen. The proton will
A. Go straight into the
wire.
B. Hit the wire in front
of the screen.
C. Hit the wire behind
the screen.
D Be
D.
B deflected
d fl t d over
the wire.
E Be deflected under
E.
the wire.
Physics 201: Lecture 1, Pg 7
Clicker Question 2:
Which magnetic field causes the observed force?
Physics 201: Lecture 1, Pg 8
Clicker Question 3:
A long straight wire is carrying current from left to right. Near the wire
is a charge
g q with velocity
y v. C
Compare
p
the strength
g of the magnetic
g
force on q in (a) vs. (b)
a) (a) has the larger force
b) (b) has the larger force
c) force is the same for (a) and (b)
v
a)
I
r
v
b)
r
I
Physics 201: Lecture 1, Pg 9
Electric vs Magnetic
Electric
Magnetic
Source:
Charges
Moving Charges
Act on:
Charges
Moving Charges
Magnitude:
F=Eq
F = q v B sin()
Direction:
Parallel E
Perpendicular to v,B
Physics 201: Lecture 1, Pg 10
M ti off q in
Motion
i uniform
if
B field
fi ld
x x x x x x x
R
• Force is perpendicular to B,v
• Uniform circular motion
• B does no work!
• (W=F d cos )
• Speed is constant
• (W=
(W  K.E.
KE )

Calculate R
v
x x x x x x x
v2
F m
R
v2
qvBsin θ  m
qvBsin
R
x x x x x x x
F
v
x x x x x x x
F
x x x x x x x
x x x x x x x
Uniform B into page
x x x x x x x
mv
R
qB
Physics 201: Lecture 1, Pg 11
Particle Moving in an External B-Field

If the particle’s
velocityy is not
perpendicular to the
field, the path
followed by the
particle is a spiral
 The spiral
p
p
path is
called a helix
Physics 201: Lecture 1, Pg 12
Aurora
Physics 201: Lecture 1, Pg 13
Clicker Question 4:
Each chamber has a unique magnetic field. A positively charged
particle enters chamber 1 with velocity 75 m/s up, and follows the
dashed trajectory.
What is the direction of the magnetic field in region 1?
a)) up
p
b) down
c) left
d) into page
e) out of page
1
2
v = 75 m/s
/
q = +25 mC
Physics 201: Lecture 1, Pg 14
Clicker Question 5:
Each chamber has a unique magnetic field. A positively charged
particle enters chamber 1 with velocity 75 m/s up, and follows the
dashed trajectory.
Compare the magnitude of the magnetic field in chambers 1 and
2
A) B1 > B2
B) B1 = B2.
C) B1 < B2
2
1
v = 75 m/s
/
q = +25 mC
Physics 201: Lecture 1, Pg 15
Clicker Question 6:
Each chamber has a unique magnetic field. A positively charged
particle enters chamber 1 with velocity 75 m/s up, and follows the
dashed trajectory.
What is the speed of the particle in chamber 2.
A) v2 < 75 m/s
/
B) v2 = 75 m/s
C) v2 > 75 m/s
2
1
v = 75 m/s
/
q = +25 mC
Physics 201: Lecture 1, Pg 16
Force on a Current


F = q v B sin()
Out of the page (RHR)
+
• F =(q/t)(vt)B sin()
= I L B sin()
Flat right hand rule

v
B
+ + + +
v
I = q/t
L = vt
Physics 201: Lecture 1, Pg 17
Clicker Question 7:
Suppose a current pointing up is applied
applied.
In which direction will the wire feel a force?
((a)) Right
Ri ht
(b) Left
(c) Out of the page
(d) Into the page
(e) There will be no force
Physics 201: Lecture 1, Pg 18
Force between wires carrying current
I towards us
B
•
•
Another I towards us
F
Conclusion: Currents in same direction attract!
I towards us
•
B

F
Another I away from us
Conclusion: Currents in opposite directions repel!
Note: this is different from the Coulomb force between like or unlike
charges.
Physics 201: Lecture 1, Pg 19
Clicker Question 8:
What is the direction of the force on the top wire, due to the two
b l ?A
below?
Assume th
the wires
i
carry equall magnitude
it d off currentt
A.
B.
C
C.
D.
E.
Left
Right
Up
Down
Zero
Physics 201: Lecture 1, Pg 20
Example:

The wires are located at ((-2,0)
2 0) meters and (2
(2,0)
0)
meters. The former carries 3 A coming out from the
sheet of the paper, and the latter 3 A going into it.
What is the xx-component
component of the force on a 5
5-metermeter
long segment of wire B due to the magnetic field
from wire A?
(a) F = -2.25 × 10-6 N
(b) F = -1.25 × 10-6 N
(c) F = 0 N
(d) F = +1.25 × 10-6 N
(e) F = +2.25 × 10-6 N
Physics 201: Lecture 1, Pg 21
Example:
The wires are located at ((-2,0)) meters and ((2,0)) meters. The
former carries 3 A coming out from the sheet of the paper, and
the latter 3 A going into it. What is the x-component of the force
on a 5-meter-long
g segment
g
of wire B due to the magnetic
g
field
from wire A?
Physics 201: Lecture 1, Pg 22
Clicker Question 9:
A rectangular loop of wire is carrying current as shown. There is a
uniform magnetic field parallel to the sides ab and cd.
The loop will:
(a) move to the right
(b) move to the left
(c) move up
(d) move down
(e) rotate
B
d
a
c
b
Physics 201: Lecture 1, Pg 23
Torque on Rotated Loop
More general case

Magnitude
Di ti
Direction:
B
 = I A B sin
is angle between normal and b-field
The torque tries to line up its B-field with the external B!
Even if the loop is not rectangular, as long as it is flat
 = N I A B sin
# of loops
(area of loop)
Physics 201: Lecture 1, Pg 24
Clicker Question 10:
If released from rest, the current loop will
A.
B.
C.
D.
E.
Move upward.
Move downward.
Rotate clockwise.
Rotate counterclockwise.
Do something not listed here.
Physics 201: Lecture 1, Pg 25
MRI
Physics 201: Lecture 1, Pg 26
Magnetic Resonance Imaging
Physics 201: Lecture 1, Pg 27
Types of Magnetic Materials


Soft magnetic materials are easily magnetized
(Iron)
 Lose their magnetism easily
Hard magnetic materials are difficult to magnetize
(
(nickel)
)
 Retain their magnetism
Physics 201: Lecture 1, Pg 28
Atomic Magnets
 A plausible explanation for
the magnetic properties of
materials is the orbital motion
of the atomic electrons.
 The figure shows a simple
simple,
classical model of an atom in
which a negative
g
electron
orbits a positive nucleus.
 In this picture of the atom, the electron’s motion is that
of a current loop!
 An orbiting electron acts as a tiny magnetic dipole,
with a north pole and a south pole
pole.
Physics 201: Lecture 1, Pg 29
Magnetic Effects of Electrons – Spins

Electrons also have spin
 The classical model is to
consider
id th
the electrons
l t
tto spin
i
like tops
 It is actuallyy a q
quantum effect
Physics 201: Lecture 1, Pg 30
Magnetic Effects of Electrons –
Orbits

An individual atom should act like a
magnet because of the motion of the
electrons about the nucleus
 Each electron circles the atom once in about
every 10-16 seconds
 This
Thi would
ld produce
d
a currentt off 1
1.6
6 mA
A and
da
magnetic field of about 20 T at the center of
the circular path

However, the magnetic field produced by
one electron in an atom is often canceled
by an oppositely revolving electron in the
same atom
Physics 201: Lecture 1, Pg 31
Magnetic Effects of Electrons –
Spins, cont


The field due to the spinning is generally
stronger than the field due to the orbital
motion
Electrons usually pair up with their spins
opposite each other, so their fields cancel
each
h other
th
 That is why most materials are not
naturally magnetic
Physics 201: Lecture 1, Pg 32
Magnetic Effects of Electrons –
Domains

In some materials
materials, the spins do not
naturally cancel
 Suc
Such materials
ae asa
are
e ca
called
ed ferromagnetic
e o ag e c


Large groups of atoms in which the spins
are aligned are called domains
When an external field is applied, the
domains that are aligned with the field
t d tto grow att the
tend
th expense off the
th others
th
 This causes the material to become
magnetized
Physics 201: Lecture 1, Pg 33
Domains, cont


Random alignment, a, shows an
unmagnetized material
When an external field is applied, the
domains aligned with B grow, b
Physics 201: Lecture 1, Pg 34