# 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?

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E=2k*lembda/r

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

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Suppose proton stops at x m from line of charge

Work done by electric field = kinetic energy

work =qU=KE

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

-(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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