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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
B--fields
 Adding magnetic fields
 Force between wires
Physics 202: Lecture 9, Pg 1
The Magnetic Force on a Moving Charge
The magnetic force turns out to depend not only on
the charge and the charge’s velocity, but also on
how the velocity vector is oriented relative to the
magnetic field
field.
Physics 202: Lecture 9, Pg 2
The Magnetic Force on a Moving Charge
The magnetic force turns out to depend not only on
the charge and the charge’s velocity, but also on
how the velocity vector is oriented relative to the
magnetic field
field.
Physics 202: Lecture 9, Pg 3
The Magnetic Force on a Moving Charge
The magnetic force turns out to depend not only on
the charge and the charge’s velocity, but also on
how the velocity vector is oriented relative to the
magnetic field
field.
Physics 202: Lecture 9, Pg 4
Force on charged particle by BB-field
The magnetic force on a charge q as it moves
through a magnetic field B with velocity v is:
where  is the angle between v and B.
Physics 202: Lecture 9, 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 202: Lecture 9, Pg 6
Examples
Physics 202: Lecture 9, Pg 7
Give it a try:
The direction of the magnetic force on the proton is
A.
B
B.
C.
D
D.
E.
To the right.
T the
To
th left.
l ft
Into the screen.
O t off the
Out
th screen.
The magnetic force
is zero.
Physics 202: Lecture 9, Pg 8
M ti off q in
Motion
i uniform
if
B field
fi ld

Calculate R
2
v
F m
R
v2
qvBsin θ  m
qvBsin
R
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
R
F
v
v
x x x
F
• Force is perpendicular to B,v
• Uniform circular motion
• B does no work!
• (W=F d cos )
• Speed is constant
• (W= K.E. )
x x
x x x x x x x
Uniform B into p
page
g
x x x x x x x
mv
R
qB
35
Physics 202: Lecture 9, Pg 9
Clicker Question 8:
A magnetic field B= 1.3×10
1 3×10-33 T pointing directly into
the screen is used to protect a wall from damage
due to incident particles of mass m = 3×10-27 kg,
19 C, and velocity v =
positive charge q = 1.6×10-19
2×104 m/s as shown. What must the length L be?
((a)) About
Ab t 15 cm
(b) About 30 cm
(c) About 60 cm
(d) About 90 cm
(e) About 100 cm
Particle
  
  
L?
Physics 202: Lecture 9, Pg 10
Example

L=R
(3 10-27 kg) ( 2 10 4 m/s)
mv

R
(1.6 10-19 C)(1.3 10-3 T)
qB
Particle
 .2885m
R=L
     
     
L?
Physics 202: Lecture 9, 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 202: Lecture 9, Pg 12
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 202: Lecture 9, Pg 13
Give it a try:
The horizontal wire can be levitated – held up against
the force of gravity – if the current in the wire is
A. Right to left.
B. Left to right.
C. It can’t be done with
this magnetic field.
Physics 202: Lecture 9, Pg 14
No Magnetic
g
Charges
g

Magnetic Fields are created by moving electric charge!

Where is the moving charge?
Orbits of electrons about nuclei
Intrinsic “spin” of
electrons (more
important effect)
Physics 202: Lecture 9, Pg 15
The Electron Spin


An electron’s inherent magnetic moment is often
called the electron spin because,
because in a classical
picture, a spinning ball of charge would have a
magnetic moment.
While it ma
may not be spinning in a literal sense
sense, an
electron really is a microscopic magnet.
Physics 202: Lecture 9, Pg 16
Magnetic Properties of Matter
 For most elements, the
magnetic moments of
th atoms
the
t
are
randomly arranged
when the atoms join
together to form a
solid.
 As the figure shows,
this random
arrangement produces
a solid whose net
magnetic moment is
very close to zero.
Physics 202: Lecture 9, Pg 17
Ferromagnetism
 In iron, and a few
other substances, the
atomic magnetic
moments tend to all
line up in the same
direction, as shown
in the figure.
g
 Materials that behave
in this fashion are
called ferromagnetic,
with the prefix ferro
meaning “iron-like
iron like.”
Slide 32-158
Physics 202: Lecture 9, Pg 18
Ferromagnetism
 A typical piece of iron is divided
into small regions, typically less
than 100 m in size, called
magnetic domains.
 The magnetic moments of all
the iron atoms within each
domain are perfectly aligned
aligned,
so each individual domain is
a strong magnet.
 However, the various magnetic
domains that form a larger solid
are randomly
d l arranged.
d
Physics 202: Lecture 9, Pg 19
Induced Magnetic Dipole
 If a ferromagnetic substance is subjected to an external
magnetic field
field, the external field exerts a torque on the
magnetic dipole of each domain.
q causes
 The torque
many of the domains
to rotate and become
aligned
li
d with
ith th
the
external field.
Physics 202: Lecture 9, Pg 20