Question

A positive point charge is released from rest at a distance r₀ from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance r from line charge, is proportional to
(A) v ∝ e⁺ʳ/ʳ⁰
(B) v ∝ ln(r/r₀)
(C) v ∝ √ln(r/r₀)
(D) v ∝ (r/r₀)

Answer 1

the correct answer is option d

hope this helps you if please mark my ans as brainliest

Answer 2

The speed (v) of the point charge is proportional to:

(C) v ∝ √ln(r/r₀)

• The kinetic energy can be represented as ( 1 / ​2 ) mV² which will be equivalent to −q (V₂−V₁​), i.e.

        ( 1 / ​2 ) mV² = −q (V₂−V₁​)

• Also, E = λ / 2πε₉​r​

• Now, ΔV = λ​ℓnr₀ / 2πε₀r

• Thus, ( 1 / ​2 ) mV²  = ₋qλ​ℓnr₀ / 2πε₀r                         (  ΔV  = V₂−V₁​  )

• Hence, v ∝ √ln(r/r₀)

​