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

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

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

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