Chapter 21
MAGNETIC FORCES AND MAGNETIC FIELDS
magnetic field

condition of space around
magn
et in which another magnet
experience
s force; m
agnetic poles

north
or
south
,
like poles repel each other, unlike poles attract;
magnetism is caused by moving
charges,
(
current in
a wire
);
moving charge or c
urrent

carrying wire produces magnetic field, and
experience
s a force if placed in
external magnetic field.
S
ections
1
–
5, 7, 8, and 10
Problems 2, 12, 15, 21, 33, 35, 53, 59, 69, 75
electromagnet
a
magnet with a field produced by an electric current
law of poles
like poles repel each other and unlike poles attract
magnetic domain
cluster of magnetically aligned atoms
magnetic field
the space around a magnet in which another magnet or moving char
ge will experience a force
mass spectrometer
a device which uses forces acting on charged particles moving a magnetic field and the
resulting path of the particles to determine the relative masses of the charged particles
right

hand rules
used to find t
he magnetic field around a current

carrying wire or the force acting on a wire or
charge in a magnetic field
solenoid
a long coil of wire in the shape of a helix; when current is passed through a solenoid it produces a
magnetic field similar to a bar magn
et
B
= magnetic field
F
B
= magnetic force
q
= charge
v
= speed or velocity of a charge
θ
= angle between the velocity of a
moving charge and a magnetic field,
or between the
length of a current

carrying wire and a magnetic field
r
= radius of path
of a charge moving in
a magnetic field, or radial distance
from a current

carrying wire
m
= mass
I
= current
L
= length of wire in a magnetic field
μ
0
= permeability constant
= 4π x 10

7
(T m) / A
Sections
21.2, 21.3, and 21.4
The Force That a Magnetic Field Exerts on a Moving Charge, The
Motion of a Char
ged Particle in a Magnetic Field, and The Mass Spectrometer
moving charge creates
magnetic field around itself,
feel a force when move through magnetic field,
direction of
force acting on charge

right

hand rule,
thumb pointing in direction of velocity
of charge
right hand for m
oving positive charges, and
left hand for moving negative charges.
Right

hand Rule
No. 1
for force on a moving charge
:
Place fingers in direction of
magnet
ic field
(north to south), thumb in direction of
velocity of a mo
ving charge
(or current in a wire), and
magnetic force on
charge (or wire) will come out of your palm.
B
F
I or
v
N
S
v
B
F
equation for finding force on a charge mo
ving through a magnetic field
F = qvBsin
q

charge in
Coulombs,
v

velocity in m/s,
B

magnetic field i
n Teslas,

ang
le between the velocity and
magnetic field. If
angle is 90
,
equation becomes
F = qvB.
Example 1
A proton enters
a magnetic field
B
which is directed into the page. The proton has a charge
+q
and a
velocity
v
which is directed to the r
ight, and enters the magnetic field perpendicularly.
q
= +1.6 x 10

19
C
v
= 4.0 x 10
6
m/s
B
= 0.5 T
Determine
(a) the magnitude and direction of the initial force acting on the proton
(b) the subsequent path of the proton in the magnetic field
(
c) the radius of the path of the proton
(d) the magnitude and direction of an electric field that would cause the
proton to continue moving in
a
straight line.
21.5 The Force on a Current in a Magnetic Field
current

carrying wir
e creates
magnetic field
around itself according to first right

hand rule, every
current

carrying wire is a magnet;
plac
e a current

carrying wire in
external magnetic fiel
d, experience
a force,
t
he direction of force acting on
wir
e is given by
right

hand rule
:
left
hand to
find direction of
magnetic force

electron flow
instead of conventional current, equation
finding
force on
current

carr
ying wire in
magnetic field
F = ILBsin
I

current
,
L

length of
wire
,
B

magnetic field,

angle be
tween le
ngth of wi
re and magnetic field;
angle

90
equation
F
= ILB.
E
xample
2
A
wire carrying a 20 A current and having a length L = 0.10 m
is placed
between the poles of a
magnet at an angle of 45
, as shown. The magnetic field i
s uniform and has a value of 0.8 T.
v
B
q
N
S
I
B
B
F
I or
v
Determine
the magnitude and direction of the ma
gnetic force acting on the wire.
(
sin 45
= cos 45
= 0.7
)
HINT
direction of
f
orce can be found by
right

hand rule; Place fingers in
direction o
f magnetic field,
thumb in direction of length (an
d current) perpendicular to
magnetic field, the force is
out of the page
.
Note
length must have a component
perpendicular to
magnetic field, or
no magnetic force on wire,
wire is placed parallel to the magnetic field, sin 0
= 0, force

zero.
Remember
r
ight
hand for current or (
positive charges
)
, and
left
h
and for electron flow or (negative
charges)
Example 3
A
wire
is bent
in
to a square loop
and placed completely in a magnetic field
B
= 1.2 T.
Each side of the
loop has a length of 0.1m and
the current
passing
through the loop
is 2.0 A.
The loop and magnetic
field is in the plane of the page.
(a) Find the magnitude of the
initial
force on
each side of the wire.
(b) Determine the initial net torque acting on the
loop.
21.7 and 21.8 Magnetic
Fields Produced by Currents, and Ampere’s Law
current

carrying wire creates magnetic field around;
magnetic fields

produced by moving charges;
why all atoms are tiny magne
ts, electrons around
nucleus of
atom are moving charges
,
therefor
e
magnetic; magn
etic field due to
current

car
rying wire circulates around
wire in a direction

found by
another right

hand rule.
Right

hand Rule
No. 2
for the magnetic field around a current

carrying wire:
Place your thumb in the direction of the current
I
, and your fi
ngers will curl around in the direction of
the magnetic field produced by that current.
determining
direction
of a magnetic field due to flow of electrons in
wire, use the left hand instead of
the right hand.
distance
r
from th
e wire is small com
pared to length of
wire, find magnitude of
magnetic field
B
by
equation
I
B
N
S
45
Top View
a
b
c
d
B
I
current I
Magnetic Field
B
I
o

permeability constant
=
4
x 10

7
4

constant
,
magnetic field around
current

carrying
wire is proportional to
,
electric field around
point charge is proportional to
.
Free Response Question:
Two wires cross each other at right angles. The vertical wire is carrying a current
I
and the horizontal wir
e is
carrying a current 4
I
. Point P is a perpendicular distance
r
from the vertical wire, and a distance 2
r
from the
horizontal wire.
(a) With reference to the coordinate system shown at the right, d
etermine the magnitude and direction of the
magnetic fi
eld at point P.
An electron is moving parallel to the horizontal wire with a speed
v
in the
+x
direction. Determine each of the
following as the charge passes point P:
(b)
the magnitude and direction of the net force acting on the electron
(c) the magnitude and direction of the electric field necessary to keep the electron moving in a straight horizontal
path.
r
2r
4I
I
P
x
y
+z
(out of page)
I
r
r
2r
4I
I
P
e
v
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