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    A proton in a well

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    The figure [attached] shows electric potential V along an x axis. A proton is to be released at x = 3.5 cm with initial kinetic energy 3.5 eV. The scale of the vertical axis is set by Vs = 10.0 V.

    (a) If it is initially moving in the negative direction, it either reaches a turning point (if so, what is the x coordinate of that point) or it escapes from the plotted region (if so, what is its speed at x = 0)?

    (b) If it is initially moving in the positive direction, it either reaches a turning point (if so, what is the x coordinate of that point) or it escapes from the plotted region (if so, what is its speed at x = 6.0 cm)?

    (c) What is the electric force (including sign) on the proton if the proton moves just to the left of x = 3.0 cm?

    (d) What is the electric force (including sign) on the proton if the proton moves just to the right of x = 5.0 cm?

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    https://brainmass.com/physics/energy/proton-well-522586

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    The particle is a proton.
    Thus, the potential energy of such a particle under potential V(x) is simply
    (1.1)
    Where e is the charge of an electron.
    First, let's express the potential energy in mathematical terms:
    (1.2)
    Where is given in electron-volts while x is given in centimeters.
    The proton has initial kinetic energy at , so the total mechanical energy is:
    (1.3)
    The total mechanical energy is constant, so for any x:
    (1.4)

    In our case and , thus so the total mechanical energy is:
    (1.5)
    If we plot the potential and total mechanical energy on the same graph it looks like:

    A turning point occurs when the total energy equals the potential energy.
    If initially the ...

    Solution Summary

    The expert examines protons in a well with an electric potential.

    $2.19

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