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 C  U = -9V x Joules  U = -9 microJoules Potential energy is lower by 9 microJoules

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

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