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Infinitely long line of charge

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An infinitely long line of charge has linear charge density 4.50Ã—10^-12 Coulombs/m. A proton (mass 1.67Ã—10^-27 kg, charge 1.60Ã—10^-19 C) is 12.5 cm from the line and moving directly toward the line at 3000 m/s.

1) Calculate the proton's initial kinetic energy in J.
2) How close, in metres, does the proton get to the line of charge?

https://brainmass.com/physics/electric-magnetic-fields/infinitely-long-line-charge-165156

Solution Preview

1) Initial kinetic energy of the proton = Â½ mv^2 = Â½ x 1.67Ã—10&#8722;27 x 3000^2 = 7.5 x 10^-21 J

2) Electric field at a distance r from an infinite uniformly charged line = E = 2&#963;/(4&#928;&#1028;or)
where &#963; is the linear charge density. In this case :

E = (2 x 4.50Ã—10^&#8722;12)(9x10^9)x1/r = ...

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