How close does the proton get to the line of charge?

An infinitely long line of charge has linear charge density 4.50×10−12 Cm. A proton (mass 1.67×10−27 , charge 1.60×10−19 C) is 16.5cm from the line and moving directly toward the line at 1000m/s .

A) Calculate the proton’s initial kinetic energy.

B) How close does the proton get to the line of charge?

2 Answers

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    Potential difference = dU = -Edr= -(2k*lembda/r)dr

    Potential difference = U = -(2k*lembda)ln(r)

    K.E of proton =0.5mv^2= 8.35*10^-22 J

    A) The proton’s initial kinetic energy is 8.35*10^-22 J


    Suppose proton stops at x m from line of charge

    Work done by electric field = kinetic energy

    work =qU=KE


    -(2k*lembda)ln(r)=8.35*10^-22 /1.6*10^-19

    ln(r1) - ln(r2) = - 5.21875*10^-3 / 2k*lembda

    ln(r1) - ln(r2) = - 5.21875*10^-3/2k*lembda

    ln(r1) - ln(r2) = - 5.21875*10^-3/2*9*10^9*4.5*10^-12

    ln(r1) - ln(r2) = -0.064429

    ln(r1 /r2) = -0.064429

    (r1 /r2) =0.9376

    r1 = 0.165 *0.9376=0.1547m

    B) The proton gets up to 15.47 cm or 0.1547 m from the line of charge

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