An infinitely long line of charge has linear charge density 5.00 10-12 C/m. A proton (mass 1.67 10-27 kg, charge + 1.60 10-19 C) is 18.0 cm from the line and moving directly toward the line at 1.20 103 m/s. How close does the proton get to the line of charge?

Question

Kristin Holder

Physics

2 November, 03:30

An infinitely long line of charge has linear charge density 5.00 10-12 C/m. A proton (mass 1.67 10-27 kg, charge + 1.60 10-19 C) is 18.0 cm from the line and moving directly toward the line at 1.20 103 m/s. How close does the proton get to the line of charge?

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Answers (1)

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Shepherd · Answer 1

Answer: 16.57cm

Explanation:

Given

λ = 5*10^-12C/m

Mass, m = 1.67*10^-27kg

v = 1.2*10^3

Ri = 18cm

K = ?

Rf = ?

K = mv²/2

K = (1.67*10^-27) * (1.2*10^3) ²/2

K = 1.2*10^-21J

Recall, Vf - Vi = K/e

Vf - Vi = 1.2*10^-21/1.6*10^-19

Vf - Vi = 7.5*10^-3

Vf - Vi = 0.0075

Also, Vf - Vi = (λ/2πE) [In (Rf/Ri) ]

In Rf/Ri = (-0.0075*2*π*8.85*10^-12) / 5*10^-12

In Rf/Ri = - 0.083

Rf = Ri (exp - 0.083)

Rf = 18 (exp - 0.083)

Rf = 16.57 cm

the proton gets as close as 16.57cm to the line of charge