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Electric Potential Energy And Electric Potential • Gravitational forces store mechanical work in the form of potential energy ( PE) • Mechanical work that is stored as electric energy is called electric potential energy When is mechanical work done in an electrical system? When is mechanical work done in an electrical system? Opposite charges Like charges Separating two charges that attract each other requires mechanical work. • Moving two charges that repel each other closer together requires mechanical work Work is stored in the electric field as electric potential energy • This work is stored in the electric fields as electric potential energy. Calculating work done in an Electric Field • In an Uniform electric field. • +q is placed in the field and experiences a downward electrical force ( F = qE) • When charged is moved upwards ( distance d) -- electric force and displacement are in opposite direction • Work done by electric force is negative and equal in magnitude to the force times distance. • W=-qEd Equation for Work and potential energy • Δ PE = -W Gives a direct connection between the work done to move charges in an electric field and the system’s change in electric potential energy: • Δ PE = -W • Δ PE = q E d Electric potential energy increases in this case. Like raising the ball against the force of gravity. Voltage is the electric potential energy per charge • Electric Potential, V • Change in electric potential = Change in electric potential energy • charge • Δ V = Δ PE / q • SI unit: joules/ coulomb = Volt ( V ) • Volt is named after Alessandro Volta who invented the battery. Units of Voltage • The volt has the units of energy ( J ) per charge ( C) • 1 V = 1 J/C 1 joule of energy is equal to 1 coulomb times 1 volt 1J=(1C)(1V) • A 1.5 V battery does 1.5 j work for every coulomb of charge • ( 1 C ) ( 1.5 V ) = 1.5 J What is the change in electric potential energy ? • Find the change in electric potential energy, Δ PE , as a charge of 2.20x10-6C moves from point A to point B, given that the change in electric potential between these points is ΔV=24.0V Find the change in electric potential energy, Δ PE , as a charge of 2.20x10-6C moves from point A to point B, given that the change in electric potential between these points is ΔV=24.0V • Using • ΔPE = q Δ V 2.20x10-6 C) ( 24.0 V) • = 5.28x10-5 J • =( Widely separated unlike charges produce high voltage because they store a lot of energy . Like charges close together produce high voltage because they store a lot of energy. Electric potential is related to the electric field • The magnitude W = q E d • Therefore the change in electric potential is • Δ V = Δ PE / q = -W/q = - (q Ed) q = -Ed Connection between Electric field and the Electric Potential • Electric field = - change in electric potential distance E=ΔV/d SI units: volts / meter (V/m) • Charge q moves in the direction of the electric field,( E ) a distance (d). • Electric potential (V) decreases by the amount • Δ V = -Ed • Electric field depends on the rate of change of the electric potential with position Gravitational analogy for electric potential (V) and electric field (E) Uniform electric field The electric potential (V) decrease as q moves in the direction of the electric field . In this case the electric field is constant, electric potential decreases uniformly with distance. Relative to the electric field in what direction does the electric potential decrees? • The electric potential decreases in the direction of the electric field. • Electric potential does’t change at all in the direction perpendicular to the electric field.