An electron is rotating around an infinite positive linear charge in a circle of radius 0.1m, if the linear charge density is 1 micro coulomb per metre , then the velocity of electron in m/s will be??
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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₎)
Now put all the values, we get:
v = √(1.6x10⁻¹⁹)(10⁻⁶)(2)(3.14)/9.1x10⁻³¹
v = 1.05x10³ m/s
which is the required answer.
Thanks.
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₎)
Now put all the values, we get:
v = √(1.6x10⁻¹⁹)(10⁻⁶)(2)(3.14)/9.1x10⁻³¹
v = 1.05x10³ m/s
which is the required answer.
Thanks.
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