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 = σ 2 ϵ 0 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 → = - c k ^ with

Step-by-step solution

For the particle to reach at origin, work done by the force should be greater than the increase in the potential energy of the charged particle. Therefore, c z ≥ σ q 2 ϵ 0 R - R 2 + z 2 - z ⇒ c 2 ϵ 0 σ q ≥ R - R 2 + z 2 - z z ⇒ β ≥ R - R 2 + z 2 - z z For option A R - R 2 + z 2 - z z = R - R 1 + 625 49 - 25 7 R 25 7 ≃ 0 . 242 Since, 0 . 25 > 0 . 242 Option A is correct. For option B R - R 2 + z 2 - z z = R - R 1 + 9 49 - 3 7 R 3 7 ≃ 0 . 79 Sin