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15 April, 09:51

An electron moving with a velocity of 1.1 ✕ 106 m/s along the positive y-axis encounters a uniform B-field of 6.0 T oriented along the negative z-axis. Find the force on this charged particle due to this magnetic field.

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  1. 15 April, 10:12
    0
    Answer: 1.057*10^-12 N, towards the negative x axis

    Explanation: An electron moving in a uniform magnetic field experiences a force.

    This force is defined by the formulae below.

    F = qvB sinx°

    Where F = force on electronic charge

    q = magnitude of electronic charge = 1.602*10^-19c

    v = velocity of electron = 1.1*10^6 m/s

    B = strength of magnetic field = 6.0T

    x° = angle between the velocity of the electron and strength of magnetic field = 90° (this is because the axis of the Cartesian plane are perpendicular)

    By substituting the parameters, we have that

    F = 1.602*10^-19 * 1.1*10^6 * 6 * sin 90

    F = 1.602*10^-19 * 1.1*10^6 * 6 * 1

    F = 1.057*10^-12 N

    The direction of this force is gotten by using cross product on the direction of the velocity and the magnetic field.

    Magnetic field is directed towards the negative z axis (-k) and velocity is directed towards the positive y axis (j)

    j * (-k) = - i

    Hence the force is directed towards the negative axis
  2. 15 April, 10:16
    0
    10.56*10^-13N

    Explanation:

    From the question, the electron and the magnetic field are perpendicular and make an of 90° with each other.

    Force on the electron = qvBsinø

    q = magnitude of charge on the electron = 1.6*10^-19C

    v = velocity of the electron = 1.1*10^6 ms-1

    B = magnetic field intensity = 6.0T

    Ø = angle between electron and magnetic field=90°

    F = 1.6*10^-19 * 1.1*10^6*6.0 * sin 90°

    F = 10.56*10^-13N
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