A research Van de Graaff generator has a 360 m diameter meta

A research Van de Graaff generator has a 3.60 m diameter metal sphere with a charge of 1.08 mC on it. What is the electric potential on the surface of the sphere? At what distance from its center is the potential 3.00 MV? An oxygen atom with three missing electrons is released near the surface of the Van de Graaff generator. What it its kinetic energy in MeV at the distance determined in part (b)? What is the total charge of an oxygen atom with 3 electrons missing? How is electric potential related to electric potential energy? MeV

Solution

a) the electric potential at the surface of the van de graff generator is

                                                                        V = kQ/ R   ; Q and R are the charge and radius of the generator

                                                                           = 8.89 * 10^9 * 1.08 * 10^-3 C / 1.8 m

                                                                         = 5.388 *10^ 6 volt

b) if the potential is V = 3.0MV = kQ / R

                                      R = k * Q / 3.0 * 10^6 V

                                         = 8.89 * 10^9 * 1.08 * 10^-3 / 3.0 * 10^6

                                         = 3.232 m

c) the charge on the oxygen atoms with 3 missing electrons is q = + 3 *e ; e is the charge on electron

                                                                                                           = 3 * 1.602 * 10^-19 C

                                                                                                           = 4.806 * 10 -19 C

the kinetic energy KE of the Oxygen atom must be equal to the potential energy of the potential energy of the charge placed on the surface of the generator

                     KE = electric potential energy = k * Q * q / R   ; Q and q are the charges of generator and oxygen atom

                                                                     = 8.89 * 10^9 * 1.08 * 10^-3 C* 4.806*10^-19 / 1.8 m

                                                                    = 4.315*10-9 Joules