A particle of charge q and mass m is subjected to an electric field E = E₀(1 − ax²) in the x-direction, where a and E₀ are constants. Initially the particle was at rest at x = 0. Other then the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is:

Option 1 - √(3/a)

Option 2 - √(1/a)

Option 3 - a

Option 4 - √(2/a)

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Answered by

Vishal Baghel | Contributor-Level 10

4 months ago

Correct Option - 1

Detailed Solution:

E = E? (1 − ax²)

F = qE?
acceleration = F/m = (qE? /m) (1 - ax²) = v (dv/dx)
(qE? /m) ∫? (1 - ax²)dx = ∫? vdv; (qE? /M) (x - ax³/3) = 0
x (1 - ax²/3) = 0; x = 0 & x = √ (3/a)

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