1. Examples In a 9 volt battery, typically used in IC circuits, the positive terminal has a potential 9 v higher than the negative terminal. If one micro-Coulomb of positive charge flows through an external circuit from the positive to negative terminal, how much has its potential energy been changed? q = -9V x 10 -6 C  U = -9V x 10 -6 Joules  U = -9 microJoules Potential energy is lower by 9 microJoules

2. Examples A proton is placed in an electric field of E=10 5 V/m and released. After going 10 cm, what is its speed? Use conservation of energy. a b + E = 10 5 V/m d = 10 cm  V = V b – V a = -Ed  U = q  V  U +  K = 0  K = -  U  K = (1/2)mv 2 (1/2)mv 2 = -q  V = +qEd

3. Hydrogen atom. What is the electric potential at a distance of 0.529 A from the proton? V = kq/r = 8.99*10 9 N m 2/ /C 2 * 1.6*10 -19 C/0.529*10 -10 m V = 27. 2 J/C = 27. 2 Volts Electric potential due to a positive point charge + - r r = 0.529 A 1A =10 -10 m What is the electric potential energy of the electron at that point? U = qV= (-1.6 x 10 -19 C) (27.2 V)= - 43.52 x 10 -19 J or - 27.2 eV where eV stands for electron volts Total energy of the electron in the ground state of hydrogen is - 13.6 eV Also U= 2E = -27.2 eV. This agrees with above formula.