Please show work and explain Thank you An electron is launch

Please show work and explain. Thank you

An electron is launched with initial velocity of 1.75 X 10^7 m/s from the positive plate towards the negative plate of a capacitor having radii of 7.50 cm and separation distance of 2.50 mm. If it has just enough speed to get to the negative plate, what is the charge density ?; on each plate?

Solution

the acceleration is,

a = v^2 / 2d = 1.75x10^7 * 1.75x10^7 /2*2.5*10^-3

= 6.125e+16 m/s^2

the electric field is,

E = F/q

E = ma/q = 9.11*10^-31 * 6.125e+16 / 1.6X10^-19

= 3.4874e+5 N/C

The charge density is,

charge density = e₀E = 8.85X10-12 * 3.4874e+5 = 3.086e-6 C/m^2