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Show that the orbital magnetic dipole mo...

Show that the orbital magnetic dipole moment of a revolving electron is` evr//2. `

Text Solution

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Let, r, v and T be the orbital radius, speed and period of motion of the electron.
Then, `" "T=(2pir)/(v)`
The orbital motion of the electron constitutes a loop of conventional current I in the opposite sense of its revolution.
`I=(e)/(T)=(ev)/(2pir)`
So the magnetic dipole moment associated with this electronic current loop is given by
`M_(o)=IxxA=("ev")/(2pir)xxpir^(2)=(1)/(2)xxevr`
`implies" "=("evr")/(2)`
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Knowledge Check

  • Magnetic dipole moment of revolving electron is

    A
    `(eL)/(2m)`
    B
    `(e)/(2m)`
    C
    `(e)/(2ML)`
    D
    `(e)/(mL)`

  • Maghnetic dipole moment of revolving electron is

    A
    `(evr)/(2)`
    B
    `efpir^(2)`
    C
    both 'a' and 'b'
    D
    neither 'a' not 'b'

  • Magnetic dipole moment is a

    A
    Scalar quantity
    B
    Vector quantity
    C
    Constant quantity
    D
    None of these

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