A particle of charge q and mass m is subjected to an electric field E = E 0(1- ax 2) 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 :

Question

A particle of charge q and mass m is subjected to an electric field E = E 0(1- ax 2) 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 : (A) √(2/a) (B) √(1/a) (C) a (D) √(3/a)

Tardigrade Admin · Accepted Answer

E = E 0(1- ax 2) W =∫ qE dx = qE 0 ∫ limits0 x 0(1- ax 2) dx = qE 0[ x 0-( ax 03/3)] For Δ KE =0, W =0 Hence x 0=√(3/ a )

$\frac{2}{a}$

$\frac{1}{a}$

$a$

$\frac{3}{a}$

$E = E_{0} (1 - a x^{2})$
$W = \int qE d x = q E_{0} 0 \int x_{0} (1 - a x^{2}) d x$
$= q E_{0} [x_{0} - \frac{a x _{0}^{3}}{3}]$
For $Δ K E = 0, W = 0$
Hence $x_{0} = \frac{3}{a}$

a2​​

a1​​

a

a3​​

E=E0​(1−ax2) W=∫qEdx=qE0​0∫x0​​(1−ax2)dx =qE0​[x0​−3ax03​​] For ΔKE=0,W=0 Hence x0​=a3​​

$\frac{2}{a}$

$\frac{1}{a}$

$a$

$\frac{3}{a}$

$E = E_{0} (1 - a x^{2})$
$W = \int qE d x = q E_{0} 0 \int x_{0} (1 - a x^{2}) d x$
$= q E_{0} [x_{0} - \frac{a x _{0}^{3}}{3}]$
For $Δ K E = 0, W = 0$
Hence $x_{0} = \frac{3}{a}$