Download Magnetic Force

Magnetic Force
Moving Charge
 A charge in an electric field is
E
+
subject to a force.
• Charge at rest or in motion
• In the direction of field
 A charge in a magnetic field is
also subject to a force.
B
+
v
• Only charges in motion
• Perpendicular to force and
velocity
Direction of Force
force
points into
the page
 Magnetic force is another kind
 
F v
of vector multiplication.
q
+
More force
=
increasing
deflection

B
• Vector cross product yields a
vector

 
FM  qv  B
 The magnitude is qvBsinq.
 The direction points according
to the right-hand rule.
Vector Cross Product
 The vector cross product
applies to any two vectors.
  
C  A B

C
 The cross product is
perpendicular to the plane
holding the two vectors.

B

A
 The cross product is not
commutative.
• Reversing the order gives an
anti-parallel result
 
 
B  A   A B
Uniform Field
 An electromagnet produces a
3.0 T uniform magnetic field
pointing horizontally north in
the gap between its poles.
 A proton enters the field
heading north at a downward
30° angle with a speed of 5.0 x
106 m/s.
 Find the magnitude and
direction of the force.
 The magnitude is qvBsinq.
• q = 1.6 x 10-19 C
• v = 5.0 x 106 m/s
• B = 3.0 T
• Angle between v and B is 30°
• F = 1.2 x 10-12 N
 The direction is based on a
positive charge going down.
• Down cross north is east
• Force vector points east
Particle Tracks
 Particles like
electrons and
protons turn in a
magnetic field.
 Tracks are captured
on film.
 Curvature is related
to the velocity.
Fermilab photo from the 15’ bubble chamber
Circular Path
 A charge that moves
Field into page
perpendicular to a uniform field
stays perpendicular to the field.
r

F
• Uniform circular motion

a

v
mv 2
F
 qvB
r
r
mv
qB
 The magnetic force is a
centripetal force.
Cyclotron
 The proton in the earlier
example moves in a circular
path.
 Find the radius of the circle.
 The size of the circle assumes
uniform circular motion.
•
•
•
•
•
r = mv/qB
q = 1.6 x 10-19 C
v = 5.0 x 106 m/s
B = 3.0 T
m = 1.6 x 10-27 kg
• r = 1.7 x 10-2 m
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