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Math Help - Deriving a formula for magnetic

  1. #1
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    Deriving a formula for magnetic

    Hello, it says that we must derive m = qB^2r^2/2V ..(volts)
    using formula for kinetic energy and E= kq/r^2

    thanks in advance for the help
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  2. #2
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    Quote Originally Posted by joeblack437 View Post
    Hello, it says that we must derive m = qB^2r^2/2V ..(volts)
    using formula for kinetic energy and E= kq/r^2

    thanks in advance for the help
    I can't make sense of your question. Is the charge in a magnetic field? Electric field? Both? What sort of fields? Constant?

    Give all the of the question.
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  3. #3
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    A mass spectometer accelerates ions through a voltage, V, before the ions enter a uniform magnetic field, B, that makes them turn. Develop the forumla m= qB^2r^2/2V for the mass of the ion, using kinetic and charge energy. the radius of the turn is r and the charge is q
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    Quote Originally Posted by joeblack437 View Post
    A mass spectometer accelerates ions through a voltage, V, before the ions enter a uniform magnetic field, B, that makes them turn. Develop the forumla m= qB^2r^2/2V for the mass of the ion, using kinetic and charge energy. the radius of the turn is r and the charge is q
    K.E. = qV when ion enters magnetic field: \frac{mv^2}{2} = qV

    \Rightarrow mv^2 = 2 q V .... (1)

    In magnetic field: F = \frac{mv^2}{r} = q v B \Rightarrow mv = r q B

    \Rightarrow v^2 = \frac{r^2 q^2 B^2}{m^2} .... (2)

    Substitute (2) into (1): \frac{r^2 q^2 B^2}{m} = 2 q V

    and I'm sure you can make m the subject and simplify.
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