A disk of radius R with uniform positive charge density σ is placed on the x y plane with its center at the origin. The Coulomb potential along the z -axis is V ( z ) = 2 ϵ 0 σ ( R 2 + z 2 − z )

Question

A disk of radius R with uniform positive charge density σ is placed on the x y plane with its center at the origin. The Coulomb potential along the z -axis is V ( z ) = 2 ϵ 0 ​ σ ​ ( R 2 + z 2 ​ − z ) . A particle of positive charge q is placed initially at rest at a point on the z axis with z = z 0 ​ and z 0 ​ > 0 . In addition to the Coulomb force, the particle experiences a vertical force F = − ck with c > 0 . Let β = q σ 2 c ∈ 0 ​ ​

TestHub · Accepted Answer

W e l ​ + W e x t ​ = k f ​ − k i ​ q v i ​ − q v f ​ + W e x t ​ = k f ​ − k i ​ 2 ε 0 ​ q σ ​ ( R 2 + Z 2 ​ − Z ) − 2 ε 0 ​ q σ R ​ + CZ = k f ​ C = 2 ε 0 ​ q σ β ​ Substitute β and Z, calculate K.E at Z=0 If K.E is positive ,then particle willk reach at origin. If K.E is negative ,then particle will not reach at origin.

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