A small sphere with mass 500107 kg and charge 800 C is relea

A small sphere with mass 5.00×107 kg and charge +8.00 C is released from rest a distance of 0.300 m above a large horizontal insulating sheet of charge that has uniform surface charge density = +8.00 pC/m2.

Using energy methods, calculate the speed of the sphere when it is 0.100 m above the sheet.

Solution

E = surface charge density / 2 epsilon₀

= 8 * 10^-12 / 2 * 8.854 * 10^-12 = 0.452 V/m

m g h + V q = (5 * 10^-7 * 9.8 * 0.200) + (0.452 * 0.200 * 8 * 10^-6) = 1.70 * 10^-6 J

1.70 * 10^-6 J  = m V² / 2

V = sqrt [ 2 * 1.70 * 10^-6/ 5 * 10^-7)

= 2.61 m/s