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Magnetic Forces
Forces in Magnetism

The existence of magnetic fields is known
because of their affects on moving charges.



What is magnetic force (FB)?
How does it differ from electric force (FE)?
What is known about the forces acting on
charged bodies in motion through a magnetic
field?
• Magnitude of the force is proportional to the
component of the charge’s velocity that is
perpendicular to the magnetic field.
• Direction of the force is perpendicular to the
component of the charge’s velocity
perpendicular to the magnetic field(B).
Magnetic Force (Lorentz Force)
FB = |q|vB sinθ




Because the magnetic force is always
perpendicular to the component of the
charge’s velocity perpendicular to the
magnetic field, it cannot change its speed.
Force is maximum when the charge is
moving perpendicular to the magnetic
field ( = 90).
The force is zero if the charge’s velocity is
in the same direction as the magnetic field
( = 0).
Also, if the speed is not changing, KE will
be constant as well.
Example #1

A positively charged particle traveling at
7.5 x 105 meters per second enters a
uniform magnetic field perpendicular to
the lines of force. While in the 4.0 x 10-2
tesla magnetic field, a net force of 9.6 x
10-15 newton acts on the particle. What is
the magnitude of the charge on the
particle?
FB
9.6  10 15 N
19
q


3
.
2

10
C
5
2
vB (7.5  10 )(4.0  10 T )
What is the magnetic field (B)?

The magnetic field is a force field just like electric and
gravitational fields.



It is a vector quantity.
Hence, it has both magnitude and direction.
Magnetic fields are similar to electric fields in that the field
intensity is directly proportional to the force and inversely
related to the charge.
E = FE/q
B = FB/(|q|v)
Units for B: N•s/C•m = 1 Tesla
Right Hand Rules

Right hand rule is used to determine the
relationship between the magnetic field, the
velocity of a positively charged particle and the
resulting force it experiences.
Right Hand Rules
#1
#2
FB = |q|v x B
#3
The Lorentz Force Equation &
RHR
FB = qvB sinθ
vsinθ
V
θ
Uniform B
q
What is the direction of force on the particle
by the magnetic field?
a. Right
b. Left
c. Up
d. Down
e. Into the page
f. Out of the Page
Note: Only the component of velocity perpendicular to
the magnetic field (vsin) will contribute to the force.
Right Hand Rule – What is the
Force?
x
x
x
x
x
x
x
x
x
x
x
x
x
x
v
x
+
x
x
x
x x x x x x
What is the direction of the magnetic force on the
charge?
a) Down
b) Up
c) Right
d)Left
Right Hand Rule – What is the
Charge?
Particle 1:
a. Positive
b. Negative
c. Neutral
Particle 2:
a. Positive
b. Negative
c. Neutral
Particle 3:
a. Positive
b. Negative
c. Neutral
Right Hand Rule – What is the
Direction of B
What is the direction of the magnetic field in each
chamber?
a.
b.
c.
d.
e.
f.
Up
Down
Left
Right
Into Page
Out of Page
1 4
2 3
What is the speed of the particle
when it leaves chamber 4?
a. v/2
b. -v
c. v
d. 2v
Since the magnetic force is always perpendicular to the
velocity, it cannot do any work and change its KE.
Example 2: Lorentz Force
Two protons are launched into a magnetic field with the same
speed as shown. What is the difference in magnitude of the
magnetic force on each particle?
a. F1 < F2
b. F1 = F2
c. F1 > F2
F = qv x B = qvBsinθ
Since the angle between B and the
particles is 90o in both cases, F1 = F2.
+
x
x
x
x
x
x
x
x
x
x
x
x
v1
v2
How does the kinetic energy change once the particle is in the
B field?
a. Increase
b. Decrease
c. Stays the Same
Since the magnetic force is always perpendicular to the
velocity, it cannot do any work and change its KE.
Trajectory of a Charge in a
Constant Magnetic Field

What path will a charge take when it enters a constant
magnetic field with a velocity v as shown below?
+ v
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
 Since the force is always perpendicular to the v and B, the
particle will travel in a circle
 Hence, the force is a centripetal force.
Radius of Circular Orbit
What is the radius of
the circular orbit?
x
x
x
x
x
x
Lorentz Force: F = qv x B
x
x
x
x
x
x
v2/R
x
x
x
x
x
x
x
x
x
x
x
x
Newton’s Second Law: F = mac
qvB =
mv2/R
R = mv/qB
R
Fc
v
+
Centripetal Acc: ac =
Example #2

A particle with a charge of 5.0 x 10-6 C traveling
at 7.5 x 105 meters per second enters a uniform
magnetic field perpendicular to the lines of force.
The particle then began to move in a circular
path 0.30 meters in diameter due to a net force
of 1.5 x 10-10 newtons. What is the mass of the
particle?
FB
1.5  10 10 N
11
B


4
.
0

10
T
5
6
qv (7.5  10 m / s )(5.0  10 C )
BqR (4.0 1011T )(5.0 106 C )(0.15m)
 23
m


4
.
0

10
kg
5
v
(7.5 10 m / s)
Earth’s Magnetosphere

Magnetic field of Earth’s atmosphere
protects us from charged particles
streaming from Sun (solar wind)
Aurora

Charged particles can enter atmosphere at
magnetic poles, causing an aurora
Crossed Fields in the CRT

How do we make a charged particle
go straight if the magnetic field is
going to make it go in circles?


Use a velocity selector that
incorporates the use of electric and
magnetic fields.
Applications for a velocity selector:

Cathode ray tubes (TV, Computer
monitor)
Crossed Fields
+
-
B into page



v
-
+
+
x
FxE
x
-x
x
FxB
-
v
E
-
+
+
x
x
x
x
x
x
-
-
v
-
E and B fields are balanced to control the
trajectory of the charged particle.
FB = FE
Velocity Selector
qvB = qE
v = E/B
Phosphor
Coated
Screen
Force on a Current Carrying
Wire
FB = |q|v x B = qvB sinθ
(1)
Lets assume that the charge q travels
through the wire in time t.
FB = (q)vBsinθ
When t is factored in, we obtain:
FB = (q/t)(vt) Bsinθ
Where:
q/t = I (current)
vt = L (length of wire)
Equation (2) therefore reduces to:
FB = ILB sinθ
(2)
Examples #3 & #4

A wire 0.30 m long carrying a current of 9.0
A is at right angles to a uniform magnetic
field. The force on the wire is 0.40 N. What is
the strength of the magnetic field?
FB
0.4 N
B

 0.15T
IL (9.0 A)(0.30m)

A wire 650 m long is in a 0.46 T magnetic
field. A 1.8 N force acts on the wire. What
current is in the wire?
F
(1.8 N )
I

 6.0 10 3 A
BL (.46T )(650 m)
Torque on a Current Carrying
Coil (Electric Motors/Galv.)
 = F•r
Torque on a Current Carrying
Coil (cont.)
F
•
Direction of Rotation
F
F

w
x
-F
Zero Torque
B
x
•
-F
I
-F
Max Torque
Axis of Rotation
Torque on a Current Carrying
Coil (cont.)




At zero torque, the magnetic field of the loop of
current carrying wire is aligned with that of the
magnet.
At maximum torque, the magnetic field of the
loop of current carrying wire is at 90o.
The net force on the loop is the vector sum of all
of the forces acting on all of the sides.
When a loop with current is placed in a magnetic
field, the loop will rotate such that its normal
becomes aligned with the externally applied
magnetic field.
Torque on a Current Carrying
Coil (cont.)

What is the contribution of forces from the two shorter
sides (w)?
F = IwB sin (90o – )
Note 1:  is the angle that the normal to the wire makes
with the direction of the magnetic field.
Note 2: Due to symmetry, the forces on the two shorter
sides will cancel each other out (Use RHR #1).
L
w
Axis of rotation
X
X
X
X
X
X
X
X
I
Torque on a Current Carrying
Coil (cont.)

What is the contribution of torque from the two longer
sides (L)?
F = BIL for each side since L is always perpendicular to B.
The magnitude of the torque due to these forces is:
 = BIL (½w sin) + BIL (½w sin) = BILw sin
(1)
Note: Since Lw = the area of the loop (A), (1) reduces to:
 = IAB sin
For a winding with N turns, this formula can be rewritten:
 = NIAB sin
External Magnetic
Field – Electromagnet or
permanent magnet that
provides an attractive
and repulsive force to
drive armature.
DC Motor
Split Ring Commutator –
Brushes and split ring that
provide the electrical
connection to the armature
from the external electrical
source.
DC Electric Motor
Armature – Part of the
motor that spins that
contains windings and
an iron core.
Key Ideas





Lorentz Force: A charge moving perpendicular to
a magnetic field will experience a force.
Charged particles moving perpendicular to a
magnetic field will travel in a circular orbit.
The magnetic force does not change the kinetic
energy of a moving charged particle – only
direction.
The magnetic field (B) is a vector quantity with
the unit of Tesla
Use right hand rules to determine the
relationship between the magnetic field, the
velocity of a positively charged particle and the
resulting force it experiences.