Problem

Four point charges

+8 \mu\text{C}

-1 \mu\text{C}

-1 \mu\text{C}

and

+8 \mu\text{C}

are fixed at the points

-\sqrt{27/2} \text{ m}

-\sqrt{3/2} \text{ m}

+\sqrt{3/2} \text{ m}

and

+\sqrt{27/2} \text{ m}

respectively on the

Y

-axis. A particle of mass

6 \times 10^{-4} \text{ kg}

and charge

+0.1 \mu\text{C}

moves along the

-X

direction. Its speed at

x = +\infty

v_0

. Find the least value of

v_0

for which the particle will cross the origin. Find also the kinetic energy of the particle at the origin. Assume that space is gravity free.