Question

A small sphere with mass 5.00×10−7 kg and charge +8.00 μC is released from rest a distance of 0.500 m above a large horizontal insulating sheet of charge that has uniform surface charge density σ = +8.00 pC/m2.
Using energy methods, calculate the speed of the sphere when it is 0.100 m above the sheet.

Answer 1

Work done on charge is W = Eqd = σ/(2ε₀) x q x d = {(8.00 x 10⁻¹²)/(2 x 8.854187 x 10⁻¹²)} x 3.00 x 10⁻⁶ x (0.650 - 0.250) = 5.42116402J. KE of sphere = 0.5mv² = 0.5 x 5.00 x 10⁻⁷v² = work done by E-field on charge during its fall = 5.42116402→ v = 4657 m/s.