lec23

					                          Physics I
                          Class 23



                      Magnetic Force
                    on Moving Charges


Rev. 07-Apr-04 GB
                                        23-1
    Hendrick Antoon Lorentz

               Hendrick A. Lorentz was a Dutch
               physicist who refined certain aspects of
               electromagnetic theory. He, along with
               Irish mathematical physicist George F.
               FitzGerald, deduced fundamental
               properties of the electromagnetic
               behavior of moving bodies that formed
               the basis of Einstein’s Special Theory
               of Relativity.
               The force of a magnetic field on a
               moving charge is sometimes called the
               Lorentz Force.
H.A. Lorentz
 1853-1928
                                                          23-2
    Important Facts About Velocity
    and Net Force Vectors (Review)

v                F         Same direction: speeding up.


v                F         Opposite directions: slowing down.



v
               Right angles: changing direction, same speed.
           F



                                                               23-3
Vector Cross Product (Review)


                                
             c  a  b ; | c |  | a || b | sin( )
             The direction comes from the
             right-hand rule. It is at a right
                                             
             angle to the plane formed by a
                  
             and b . In other words, the cross
             product is at right angles to both
                   
             a and b . (3D thinking required!)




                                                      23-4
Drawing 3D Vectors in 2D

                Y
  -Y   +Y


       +X                  X
 -X         Z
 -Z    +Z   +Z is out of page



                                23-5
               Magnetic Force on a
                Moving Charge
               
         F  q vB
q:
   charge of the particle (C; + or –)
v : velocity of the particle (m/s)

B : magnetic field (T)
 Force is at a right angle to velocity.
 Force is at a right angle to magnetic field.

Important: If q is negative, that reverses the direction of force.




                                                                     23-6
         An Example
An Electron in a Magnetic Field

                      Y



                          X
                  Z




                                  23-7
          Analysis of the Magnetic Force
     Y



            X
Z                                               
                                          F  q vB
                                We will evaluate this expression before
      F                         the electron starts turning.

                     
    First, evaluate v  B . In this case, they are 90° 
                                                      apart, so all we
                                                  
    need is the direction. v is +X, B is –Z, so v  B is +Y.
    Next, we need to account for q. This is an electron, so q is
    negative. Therefore, the magnitude of the force is (e v B) and the
    direction is –Y.


                                                                          23-8
            Uniform Circular Motion




As the electron turns, so does the force vector.


 Speed stays constant because acceleration is
  always perpendicular to velocity.
 The electron travels in a circle at a constant speed.



                                                          23-9
    The Radius of the Circle
F    v
         Although the directions of the vectors are
         changing, the magnitudes stay the same.
r
                    v2
         F  ma  m
                     r
         F  qvB
                 v2
         qvB  m
                  r
              v2   mv
         rm     
             qvB qB

                                                      23-10
The Period and Frequency
F   v
        The circumference of the circle is 2  r.
           Distance 2  r
r       v          
             Time     T
                     mv
                  2
           2r       qB 2m
        T             
             v      v     qB
           1    qB
        f 
           T 2m
                  qB
          2f 
                  m
                                                    23-11
              Bubble Chamber
                           The red and green lines in the figure
                           to the left are tracks of charged
                           particles in a bubble chamber. Each
                           charged particle makes a trail of
                           tiny bubbles as it moves in the
                           chamber. There is a magnetic field
                           of 1.0 T directed into the page.
        What are the signs of the charges of the particles?
   mv
r      Why do they spiral inward?
   qB
        What are they?
        What created them at the points where the tracks start?


                                                                   23-12
         The Aurora



 There is no acceleration in the direction of the
  magnetic field line. (Why?)
 The component of velocity in the direction of the
  field line remains constant. (Why?)
 The component of velocity at a right angle to the
  field line continually changes direction. (Why?)
The result is that the charged particle (electron)
travels in a spiral path along the magnetic field line,
giving off light when it hits the atmosphere.

                                                          23-13
         The Aurora
As Seen from the Space Shuttle




                             23-14
 The Effect of the Solar Wind
on the Magnetic Field of Earth




           Energetic charged particles travel along
           magnetic field lines on the sun.
           Some escape into interplanetary space.
           These are called the solar wind.
           The solar wind interacts with the magnetic
           field lines of Earth and distorts them. The
           complex interaction of flowing charged
           particles with the electromagnetic field is
           called Magneto-Hydrodynamics or MHD.
                                                         23-15
                      Class #23
                 Take-Away Concepts
1.   The magnetic (Lorentz) force on a moving, charged particle:
                  
               
         F  q vB
2. The magnetic force cannot change a particle’s speed, only the
direction of its velocity.
3. Radius and angular frequency of a charged particle in uniform
circular motion in a magnetic field:
            mv
         r
            qB
            qB
         
             m


                                                                   23-16
                     Class #23
                Problems of the Day
___1. A charged, non-magnetic particle is moving in a uniform
      magnetic field. Which of the following conditions (if any)
      would cause the particle to speed up?

A) The velocity of the particle is at a right angle to the magnetic
field.
B) The velocity of the particle is in the same direction as the
magnetic field.
C) The velocity of the particle is in the opposite direction as the
magnetic field.
D) Any of the above (A-C) would cause the particle to speed up.
E) None of the above; the magnetic force cannot cause the
particle to speed up.

                                                                      23-17
                      Class #23
                 Problems of the Day
2. An electron is traveling in a vacuum tube at 1.4 x 107 m/s in a
horizontal direction toward the south. There is a constant
magnetic field in the tube with a magnitude of 0.5 gauss. The
direction of the magnetic field is toward the north and 30º down
(toward the ground). What are the magnitude and direction of the
magnetic (Lorentz) force on the electron? (1 T = 10,000 gauss.)
                                 Up


                                                 30°
           v                S          N
                      -e
                                                       B
                                Down




                                                                     23-18
                  Activity #23
             Magnetic Field and Force

Objective of the Activity:

1.   Consider the implications of the magnetic force on speed and
     direction of a charged particle.
2.   Determine the direction and magnitude of the magnetic field at
     your table in the classroom using a compass, a coil of wire, a
     power supply, and a current meter.




                                                                      23-19

				
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posted:10/22/2011
language:English
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