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An electron is revolving around a long line charge having charge density of 2x 10 -8 C/m. Find the kinetic energy of the electron, assuming that it is independent of radius of electron’s orbit.

  1. An electron is revolving around a long line charge having charge density of 2x 10-8 C/m. Find the kinetic energy of the electron, assuming that it is independent of radius of electron’s orbit.

Grade:12

1 Answers

Khimraj
3007 Points
one year ago
Since, an electron is rotating around positive linear charge so, there will be a force of attraction among the positive charges and also since, electron is revolving in a circle there will be a centrifugal (repulsive) force acting on it.
Hence,
Centrifugal Force = Electric Force
m₍e₎ v² / r = e E
m₍e₎ v² / r = k₍e₎ Q / r²   .......... (1
Since, Q = λ . 2πr
Put in (1) :
m₍e₎ v² / r = ( k₍e₎ λ . 2πr ) / r²
v² = eλ2π/m₍e₎
v = √(eλ2π/m₍e₎)
KE = ½*m(e)v2 = eλπ = (1.6x10⁻¹⁹)(2*10⁻8)(3.14)
 

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