Question : An electron (of charge e) revolves around a long wire with uniform charge density λ in a circular path of radius r. Its kinetic energy is given by
(a) λe/2πε₀r
(b) λe/4πε₀r
(c) λe/2πε₀
(d) λe/4πε₀
Doubt by Harjas
Solution :
Solution :
We know, electric field due to an infinitely long wire of change density λ at a distance r is given by
E = λ/2πε₀r
So, the force experienced by the electron while revolving around the wire will be
F=qE
F=eλ/2πε₀r — (1)
[∵E = λ/2πε₀r]
We also know that whenever a particle revolve in a circular path it needs a centripetal force which is given by
F=mv²/r — (2)
At equilibrium
Electrostatic Force on electron (FE) = Centripetal force (FC)
eλ/2πε₀r = mv²/r
eλ/2πε₀ = mv²
eλ/4πε₀ = ½ mv²
E = λ/2πε₀r
So, the force experienced by the electron while revolving around the wire will be
F=qE
F=eλ/2πε₀r — (1)
[∵E = λ/2πε₀r]
We also know that whenever a particle revolve in a circular path it needs a centripetal force which is given by
F=mv²/r — (2)
At equilibrium
Electrostatic Force on electron (FE) = Centripetal force (FC)
eλ/2πε₀r = mv²/r
eλ/2πε₀ = mv²
eλ/4πε₀ = ½ mv²
eλ/4πε₀ = Kinetic Energy (K)
K = λe/4πε₀
K = λe/4πε₀
Hence, (d) λe/4πε₀, would be the correct option.
