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    Chap 29

    Uploaded by

    Muhammad Saqib Baig

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Chap 29

    Uploaded by

    Muhammad Saqib Baig
    2 views17 pages

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    Copyright:

    © All Rights Reserved
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    2 views17 pages

    Chap 29

    Uploaded by

    Muhammad Saqib Baig

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 17

    Magnetic Force and Field

    Chapter 29
    The magnetic force
    v parallel to the current.
    The magnitude of the magnetic force
    is directly proportional to the product
    of the current I, the charge q, and the
    speed v, and it is inversely
    proportional to the distance r.

    The minus sign in this formula


    indicates that the force is attractive if
    the charge q is positive and the
    velocity v and the current I are in the
    same direction
    if we reckon 𝑣 as positive when parallel to the current and negative
    when antiparallel, then the magnetic force is attractive if the product
    𝑞𝑣𝐼 is positive and repulsive if 𝑞𝑣𝐼 is negative.
    In the SI system of units, the numerical value of the constant of
    proportionality is exactly,

    Magnetic constant or the permeability


    constant
    v in the radial direction
    The velocity 𝑣 is directed
    perpendicularly away from the
    direction of the current. The
    magnetic force is now in the 𝒙
    direction, parallel to the direction
    of the current.
    v in the tangential direction.
    The velocity v is now directed
    tangentially to the circumference of a
    circle concentric with the current. For
    the position of the charge q at the
    instant, the direction of the velocity is
    the z direction.
    Example
    A long, straight wire carries a current of 50 A. An electron of speed
    2.0 × 106 𝑚𝑠 −1 is (instantaneously) moving parallel to this wire at a
    distance of 0.030 m. what magnetic force does the current in the wire
    exert on the electron?
    Magnetic Field
    The magnetic force is communicated from one moving charge q to
    another moving charge q through a magnetic field,
    Direction of Magnetics
    For a long wire, the direction of the magnetic field of the current is
    tangent to a circle with the current at its center.
    Direction of the magnetic field
    Right-hand rule for the
    magnetic field.

    if the thumb of the right


    hand is placed along the
    direction of the current, then
    the fingers will curl around
    the wire in the direction of
    the magnetic field.
    if the point charge moves at some general
    angle 𝛼 with respect to the magnetic field,
    only the component of its velocity
    perpendicular to the magnetic field generates
    a magnetic force,
    This right-hand rule
    Lorentz force
    If both electric and magnetic fields exert forces on a charge q, the net
    force on the charge is the vector sum of the individual forces. The
    total force due to both an electric field E and a magnetic field B is
    called the Lorentz force,


    The magnetic field B
    The direction of the magnetic field is parallel or antiparallel to that
    direction of motion that results in zero force.

    The magnitude of the magnetic field is obtained by dividing the


    magnitude of the maximum force (the force that acts when the
    motion of the test charge is perpendicular to the direction of the
    magnetic field) by the charge and the speed:
    SI unit of Magnetic Field
    The SI unit of magnetic field is N/(C.m.s), the unit of force divided by
    the unit of charge and of velocity; this unit is called the tesla (T):

    A non-SI unit of magnetic field in common use is the gauss (G):


    Example
    In Florida, the Earth’s magnetic field is in the
    north–south vertical plane (and toward the
    north), but directed downward from the
    horizontal at an angle of 58 degree (see Fig.) .
    The magnitude of this magnetic field is 5.3 ×
    10−5 𝑇. Suppose that an electron in a TV
    tube is moving with an (instantaneous)
    horizontal velocity of 𝟐. 𝟎 × 10^6 𝒎𝒔−𝟏 in
    the south to north direction. What are the
    magnitude and the direction of the force that
    the magnetic field of the Earth exerts on this
    electron?
    Representation

    Magnetic field can be


    represented graphically by
    field lines.

    The decrease of the strength


    of the magnetic field with
    distance is indicated by the
    decrease of density of the
    field line.
    Compass needle alignment with magnetic field

    Small compass needles align


    in the direction of the
    magnetic field.

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