11.22 An electron gun with its collector at a potential of 100 V fires out electrons in a spherical bulb containing hydrogen gas at low pressure ( mm of Hg). A magnetic field of 2.83 × 10–4 T curves the path of the electrons in a circular orbit of radius 12.0 cm. (The path can be viewed because the gas ions in the path focus the beam by attracting electrons, and emitting light by electron capture; this method is known as the ‘fine beam tube’ method.) Determine e/m from the data.

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    Answered by

    Payal Gupta | Contributor-Level 10

    4 months ago

    11.22 Potential, V = 100 V

    Magnetic field experienced by electron, B = 2.83 ×10-4 T

    Radius of the circular orbit, r = 12.0 cm = 12 ×10-2 m

    Mass of each electron = m

    Charge on each electron = e

    Velocity of each electron= v

    The energy of each electron is equal to its kinetic energy, i.e.

    12 m v2 = eV

    v2=2eVm …….(1)

    Since centripetal force ( mv2r) = Magnetic force (evB), we can write

    mv2r=evB

    v = eBrm ………………(2)

    Equating equations (1) and (2) we get

    2eVm=e2B2r2m2

    em = 2VB2r2 = 2×100(2.83×10-4)2×(12×10-2)2 = 1.734 ×1011 C/kg

    Therefore, the specific charge ratio (e/m) is 1.734 ×1011 C/k

    ...more

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