My
Chapter 19
Lecture
Outline
1
Chapter 19: Magnetic Forces and
Fields
•Magnetic Fields
•Magnetic Force on a Point Charge
•Motion of a Charged Particle in a Magnetic Field
•Crossed E and B fields
•Magnetic Forces on Current Carrying Wires
•Torque on a Current Loop
•Magnetic Field Due to a Current
2
§19.1 Magnetic Fields
Magnetic Dipole
All magnets have
at least one north
pole and one south
pole.
Field lines emerge from north
poles and enter through south
poles.
3
Magnets exert forces on one another.
Opposite magnetic poles attract
and like magnetic poles repel.
4
Magnetic field lines are closed loops. There is no (known!)
source of magnetic field lines. (No magnetic monopoles)
If a magnet is broken in half you just end up with two
magnets.
5
Near the surface
of the Earth, the
magnetic field is
that of a dipole.
Note the orientation of
the magnetic poles!
6
Away from the Earth, the magnetic field is distorted by the
solar wind.
Evidence for magnetic pole reversals has been found on the
ocean floor. The iron bearing minerals in the rock contain a
record of the Earth’s magnetic field.
7
§19.2 Magnetic Force on a Point
Charge
The magnetic force on a point charge is:
FB  qv  B
The unit of magnetic field (B) is the Tesla (1T = 1 N/Am).
8
The magnitude of FB is:
FB  qBv sin  
where vsin is the component of the velocity perpendicular
to the direction of the magnetic field.  represents the angle
between v and B.
v
Draw the vectors tailto-tail to determine .

B
9
The direction of FB is found from the right-hand rule.
The right-hand rule is: using your right hand, point your
fingers in the direction of the velocity v and your thumb
in the direction of the magnetic field B. The palm of your
hand points in the direction of the force F.
10
§19.3 Charged Particle Moving
Perpendicular to a Uniform B-field
  



  



  



  



  



A positively charged particle
has a velocity v (orange arrow)
as shown. The magnetic field
is into the page.
The magnetic force, at this instant, is shown in blue. In this
region of space this positive charge will move CCW in a
circular path.
11
Applying Newton’s 2nd Law to the charge:
F  F
B
 m ar
v2
qvB  m
r
12
Example: How long does it take an electron to complete one
revolution if the radius of its path is r (see the figure on slide
11)?
The distance traveled by the electron during one
revolution is d = 2r. The electron moves at constant
speed so d = vT as well. The speed of the electron can
be obtained using the result of the previous slide.
2r 2r 2me
T


eBr
v
eB
me
Is the period of the
electron’s motion.
13
Mass Spectrometer
A charged particle is
shot into a region of
known magnetic field.
B
  



  



  



  



  



Detector
2
v
Here, qvB  m
r
or qBr  m v
V
Particles of different mass will
travel different distances before
striking the detector. (v, B, and q
can be controlled.)
14
Other devices that use magnetic fields to bend particle
paths are cyclotrons and synchrotrons.
Cyclotrons are used in the production of
radioactive nuclei. For medical uses see the
website of the Nuclear Energy Institute.
Synchrotrons are being tested for use in
treating tumors.
15
§19.6 Magnetic Force on a Current
Carrying Wire
The force on a current carrying wire
in an external magnetic field is
F  I L  B
L is a vector that points in the
direction of the current flow. Its
magnitude is the length of the wire.
16
The magnitude of
F  I L  B
is
F  ILB sin 
and its direction is given by the right-hand rule.
17
Example (text problem 19.50): A 20.0 cm by 30.0 cm loop
of wire carries 1.0 A of current clockwise.
(a) Find the magnetic force on each side of the loop if the
magnetic field is 2.5 T to the left.
I = 1.0 A
Left: F out of page
Top: no force
B
Right: F into page
Bottom: no force
18
Example continued:
The magnitudes of the nonzero forces are:
F  ILB sin 
 1.0 A 0.20 m 2.5 T sin 90
 0.50 N
(b) What is the net force on the loop?
Fnet  0
19
§19.7 Torque on a Current Loop
Consider a current carrying loop in a magnetic field. The
net force on this loop is zero, but the net torque is not.
Axis
Force
into
page
Force
out of
page
B
L/2
L/2
20
The net torque on the current loop is:
  NIAB sin 
N = number of turns of wire in the loop.
I = the current carried by the loop.
A = area of the loop.
B = the magnetic field strength.
 = the angle between A and B.
21
The direction of A is defined with a right-hand rule. Curl
the fingers of your right hand in the direction of the current
flow around a loop and your thumb will point in the direction
of A.
Because there is a torque on the current loop, it must have
both a north and south pole. A current loop is a magnetic
dipole. (Your thumb, using the above RHR, points from
south to north.)
22
§19.8 Magnetic Field due to a
Current
Moving charges (a current) create magnetic fields.
23
The magnetic field at a distance r from a long, straight wire
carrying current I is
0 I
B
2r
where 0 = 4107 Tm/A is the permeability of free space.
The direction of the B-field lines is given by a right-hand
rule. Point the thumb of your right hand in the direction of
the current flow while wrapping your hand around the wire;
your fingers will curl in the direction of the magnetic field
lines.
24
A wire carries
current I out of
the page.
The B-field lines of
this wire are CCW.
Note: The field (B) is tangent to the field lines.
25
Example (text problem 19.72): Two parallel wires in a
horizontal plane carry currents I1 and I2 to the right. The wires
each have a length L and are separated by a distance d.
1
I
d
2
I
(a) What are the magnitude and direction of the B-field of
wire 1 at the location of wire 2?
 0 I1
B1 
2d
Into the page
26
Example continued:
(b) What are the magnitude and direction of the magnetic
force on wire 2 due to wire 1?
F12  I 2 LB1 sin 
 0 I1 I 2 L
 I 2 LB1 
2d
F12 toward top of
page (toward wire 1)
(c) What are the magnitude and direction of the B-field of
wire 2 at the location of wire 1?
0 I 2
B2 
2d
Out of the page
27
Example continued:
(d) What are the magnitude and direction of the magnetic
force on wire 1 due to wire 2?
F21  I1 LB2 sin 
 0 I1 I 2 L
 I1 LB2 
2d
F21 toward bottom of
page (toward wire 2)
(e) Do parallel currents attract or repel? They attract.
(f) Do antiparallel currents attract or repel? They repel.
28
The magnetic field of a current loop:
The strength of the B-field at the
center of the (single) wire loop is:
B
0 I
2R
29
The magnetic field of a solenoid:
A solenoid is a coil of wire that is wrapped in a cylindrical
shape.
The field inside a solenoid is nearly uniform (if you stay
away from the ends) and has a strength:
B  0nI
Where n = N/L is the number of turns of wire (N) per unit
length (L) and I is the current in the wire.
30
31
Summary
•Magnetic forces are felt only by moving charges
•Right-Hand Rules
•Magnetic Force on a Current Carrying Wire
•Torque on a Current Loop
•Magnetic Field of a Current Carrying Wire (straight wire,
wire loop, solenoid)
32