JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Work, Power & Energy

A particle of charge

q

and mass

m

is subjected to an electric field

E = E_{0} (1 - a x^{2})

in the x-direction, where a and

E_{0}

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:

Answer: (A)

Solution

The force on the particle is

F = q E_{0} (1 - a x^{2})

, so its acceleration is

\frac{q E _{0}}{m} (1 - a x^{2}) = v \frac{d v}{d x}

. The kinetic energy returns to zero when the work done by the force from the origin vanishes, that is when

\int_{0}^{x} (1 - a x^{2}) d x = 0

. Evaluating,

x - \frac{a x ^{3}}{3} = 0

, which apart from the starting point

x = 0

gives

1 - \frac{a x ^{2}}{3} = 0

, so

x = \frac{3}{a}

JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Single correct option