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    Infinitely long line of charge

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    An infinitely long line of charge has linear charge density 4.50×10^-12 Coulombs/m. A proton (mass 1.67×10^-27 kg, charge 1.60×10^-19 C) is 12.5 cm from the line and moving directly toward the line at 3000 m/s.

    1) Calculate the proton's initial kinetic energy in J.
    2) How close, in metres, does the proton get to the line of charge?

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    Solution Preview

    1) Initial kinetic energy of the proton = ½ mv^2 = ½ x 1.67×10−27 x 3000^2 = 7.5 x 10^-21 J

    2) Electric field at a distance r from an infinite uniformly charged line = E = 2σ/(4ΠЄor)
    where σ is the linear charge density. In this case :

    E = (2 x 4.50×10^−12)(9x10^9)x1/r = ...

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