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An infinitely long line of charge has a linear charge density of 8.00×10−12 C/m . A...

An infinitely long line of charge has a linear charge density of 8.00×10−12 C/m . A proton is at distance 17.5 cm from the line and is moving directly toward the line with speed 3000 m/s .

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

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Answer #1

given,

linear charge density = 8 * 10^-12 C/m

distance = 17.5 cm

speed = 3000 m/s

Suppose proton stops at x m from line of charge

Work done by electric field = kinetic energy

qU = KE

1.6 * 10^-19 * (-2k * lembda)ln(r) = 0.5 * 1.6726219 * 10-27 * 3000^2

-(2k * lembda)ln(r) = 7.526 * 10^-21 /1.6*10^-19

ln(r1) - ln(r2) = - 0.0470375 / 2k*lembda

ln(r1) - ln(r2) = - 0.0470375 / (2 * 9 * 10^9 * 8 * 10^-12)

ln(r1) - ln(r2) = -0.32664930555

ln(r1 /r2) = -0.32664930555

ln(r1 /0.175) = -0.32664930555

r1 = 0.126 m

distance proton can get close to line of charge = 12.6 cm

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