Applications of Particle Deflection with Moving Charges in...

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Electromagnetism Applications of Particle Deflection with Moving Charges in Magnetic and Electric Fields

Transcript of Applications of Particle Deflection with Moving Charges in...

  • Electromagnetism Applications of Particle

    Deflection with Moving Charges in Magnetic and Electric Fields

  • Review of Previous Material

  • Magnitude of Deflecting Force

    The deflecting force

    on a charged particle moving through an external magnetic field is calculated using:

    | Fm| = q v B sin θ

    where: Fm = deflecting force B =magnetic field strength (T) q = charge (C) v = speed of particle (m/s) θ = angle between v and B

    The maximum deflecting

    force will occur when θ= 90o. Thus sin 90o= 1 and Fm= qvB.

  • Example: A 20 g particle with a charge of +2.0 C

    enters 0.20 T a magnetic field at 90o to the field. If the speed of the particle is 40 m/s, what is the acceleration that is experienced by the particle in the diagram

    below?

    (2.0 )(40 / )(0.20 )

    16

    m

    m

    m

    F qv B

    F C m s T

    F N

    2 2

    16

    0.020

    800 8.0 10 /

    m net

    m

    F F

    F Na

    m kg

    a m s out of the page

  • An alpha particle enters a 50 T field at 30°to the field at a speed of 500 m/s. What is the magnitude of the deflecting force experienced by the alpha particle? (An α+2 particle has a charge of 2 x 1.60 x 10-19C = 3.2 x 10-19C.)

    19

    15

    sin

    (3.20 10 )(500 / )sin30 (50 )

    4.0 10

    m

    m

    m

    F qv B

    F C m s T

    F N

  • POS Checklist

    explain, quantitatively, how uniform magnetic and electric fields affect a moving electric charge, using the relationships among charge, motion, field direction and strength, when motion and field directions are mutually perpendicular.

  • The Movement of

    Charges Through

    Electric and

    Magnetic Fields

    Simultaneously

  • The Movement of Charges Through Electric

    and Magnetic Fields Simultaneously

    -when a charge passes through a magnetic field which is perpendicular to an electric field, it can pass through undeflected

    when no deflection of the charge occurs, the magnetic force is equal to the electrical force

    em

    e

    e m

    FE F qvB

    q

    F Eq

    F F

    Eq qvB

    E vB

    Ev

    B

  • When the forces are equal, (Fm = Fe) the

    speed of the charge can be determined

    Fm is down by 3rd

    LHR when e is in B

    Fe is up, e is attracted to the positive plate

    When Fe up = Fm down, e passes E and B undeflected

    Speed of electron can be determined

  • Example Eg) An electron enters a magnetic field of 2.00 x

    10-3 T at 90 . An electric field of 1000 N/C is perpendicular to the magnetic field. Determine the kinetic energy of the electron as it passes undeflected between the two fields.

    e mF F

    Eq qvB

    E vB

    Ev

    B

    3

    5

    2

    31 5

    19 2 2

    1000 /

    2.00 10 /

    5.00 10 /

    1

    2

    1(9.11 10 )(5.00 10 / )

    2

    1.14 10 ( / )

    k

    k

    k

    N Cv

    Ns Cm

    v m s

    E mv

    E kg m s

    E J kgm s

  • Applications of

    Magnetic Forces

  • ex) What is the velocity of a particle if the E-field is 500 N/C and the B-field is 0.75 T?

    Step 1: Determine the direction of the E and B forces.

    Step 2: Set FE equal to FB.

  • ex) Determine the charge to mass ratio of the particle using the data from previous example and given the particle deflects with r = 1.85 x 105 m.

    Step 1: Set Fm = Fc.

    Step 2: Solve for q/m.