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Ph126 Spring 2008
Lecture #8
Magnetic Fields Produced by Moving Charges
Prof. Gregory Tarlé
[email protected]
Last Lecture: Magnetic Forces

Moving charges can
experience forces in
magnetic fields:
 Magnitude:
F  q vBsin 
Direction: Right-Hand
Rule
Magnetic force does no
work on the moving charge
Measure magnetic field in
Tesla (T)



Electric vs. Magnetic Forces



The electric force is always in the direction of the
electric field, but the magnetic force is always
perpendicular to the magnetic field
The electric force acts on a charged particle
independent of the particle’s velocity, but the
magnetic force acts on a charged particle only
when it is in motion
The electric force can change the speed of a
charged particle while the magnetic force
associated with a steady magnetic field changes
the direction of the particle, but not its speed
Concept Test #1
What direction is the force this wire feels
because of the magnetic field?
Magnetic Field B
1)
2)
3)
4)
5)
6)
To the right
To the left
Up the page
Down the page
Into the page
Out of the page
Current I
Magnetic Force on a Current
F  qvB sin 
 q 
F   
vt B sin 

t

L
I
F  ILB sin 
angle between
I and B
Torque on a Current-Carrying Coil
The two forces on the loop have equal
magnitude but they are opposite in direction.
Concept Test #2
A square loop carries a current I and pivots
without friction about the z-axis. A uniform
magnetic field B points in the +x direction, and
the loop initially makes an angle θ with the x-z
plane. The torque on the loop is clockwise.


True (yes)
False (no)
Calculate the Torque
Recall :  Fr sin 
clockwise ""
Direction : 
counterclo ckwise ""
1




ILB

2 w sin  
ILB 12 w sin    IAB sin 
magnetic
moment

  NIA B sin 
N = number of
turns of wire
Max and Min Torques
The loop tends to rotate such that its normal
becomes aligned with the magnetic field
Origins of Magnetic Fields

Magnetic fields come from:
• Magnets
• Moving charges (i.e. currents)
• Changing E fields (more next lecture…)

Magnetic field lines never end; they must
form closed loops

No magnetic charges (monopoles) exist
B produced by a long straight wire
o I
B
2 r
Increases with
current, falls off
with distance
o  4 10 T  m A
7
permeability of
free space
Direction of B field of a straight
wire

The magnetic field
due to the current in
a long straight wire
has circular field
lines around the wire

The direction of the
field is given by the
right hand rule
o I
BP 
2 r
Concept Test #3
Two identical parallel long straight
wires carrying a current I stand a
distance r apart. Which of the
following statements is false?
1)
2)
3)
The magnetic field B created by
the bottom wire at P points out
of the page.
The force exerted by the
bottom wire on the top wire is
F = ILB.
The force pushes the top wire
F
up.
P
I
F
r
I
L
 o I  Lo I 2
 
 IL
 2 r  2 r
Concept Test #4
Two parallel long straight wires
carrying currents I and 2I stand a
distance r apart. Which of the
following statements is false?
1)
2)
3)
The magnetic force pulls the
top wire down toward the
bottom wire.
The magnetic force pulls the
bottom wire up toward the top
wire.
The magnetic force on the top
wire is greater than the
magnetic force on the bottom
wire.
F12
2 Lo I 2

2 r
P
I
F
r
2I
L
The force is attractive
if the currents are in
the same direction and
repulsive otherwise
the two wires generate magnetic fields that pull one
another toward each other  Newton’s 3rd Law.
Electromagnet


Current flowing in a loop of wire creates a
magnetic field
Current loop can be imagined to be a phantom bar
magnet
=
http://www.windows.ucar.edu/spaceweather/info_mag_fields.html
Which side is north pole?
 Right
hand rule
N
number of
turns
BN
S
o I
2R
At center of
circular loop
B produced by a solenoid
B  o nI
Interior of
a solenoid
number of turns
per unit length
Ampere’s Law

Ampere’s law relates sum of
B field along a line to
current inside

Formally:
 B    I
||
o
net current passing
through surface
bounded by path
B field of wire from Ampere’s Law
 B    I
||
o
B   o I
B2 r  o I
o I
B
2 r
Same as
before!
=
N
S