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Magnetic Forces
Forces in Magnetism

The existence of magnetic fields is known
because of their affects on moving charges.
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
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

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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.

Units for B: Tesla
Trajectory of a Charged
Particle in a 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.
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
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 #2 & #3

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
(1.8N )
I

 6.0 10 3 A
BL (.46T )(650 m)
Key Ideas

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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.