A very long charged wire in a particle detector (it can be approximated by an infinite...

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A very long charged wire in a particle detector (it can be approximated by an infinite line charge) has a positive linear cha

Calculate the protons initial kinetic energy.

How close is the proton to the wire when its speed equals zero?

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Answer 1

Answer #1

(a) KE_i = ½*mv²

= ½* (1.67e-27)*(4.3e3)²

= 1.54e-20 J

(b) using conservation of energy

q V = KE

q 2 ( Q/L) / ( 4 pi eo) ln ( r2/r1) = KE

(1.6* 10^-19)* 2* (6* 10^-12) * 9* 10^9* ln ( 19 / r1) = 1.54e-20

1.728e-20* ln ( 19 / r1) = 1.54e-20

ln ( 19 / r1) = 0.891

Taking antilog on both sides:

19/r1 = 2.44

=> r1 = 7.79 cm (or 0.0779 m)

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Answer 2

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