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 than the initial position, the kinetic energy of the particle becomes zero when the distance of the particle from the or…

Question

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 than the initial position, the kinetic energy of the particle becomes zero when the distance of the particle from the origin is

Accepted Answer

(4) √3/a. The particle starts at rest, so by the work-energy theorem its kinetic energy at x equals the work done by the field from 0 to x. K(x)=q∫₀^x E₀(1-ax'²) dx'=qE₀(x-(ax³)/3). Setting K=0 with x
eq0: 1-(ax²)/3=0. x²=3/a, so x=√3/a. (Up to x=1/(√a) the field accelerates the particle; beyond that it reverses and brings it back to rest at √3/a.)

Step-by-step solution

Why the other options are wrong