Lecture 09

# Lecture 09 - Potential Energy Introduced the concept of...

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Introduced the concept of electric field E to deal with forces Introduced electric potential V to deal with work and energy Electric potential: electric potential energy per unit charge Potential Energy Potential energy is associated with pairs of interacting objects A single particle has no electric potential energy

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q 1 q 2 r 12 ! E system " W int = W ext Δ U el - W int ! K system + ! U el = W ext + Q Total energy of the system can be changed ( only ) by external forces. Work done by internal forces: ! U el = " W int = " ! F int d ! r i f # Electric Potential Energy of Two Particles Energy of the system: 1. Energy of particle q 1 2. Energy of particle q 2 3. Interaction energy U el To change the energy of particles we have to perform work. ! E system = W ext + W int + Q if ! ( mc 2 ) = 0 :
The potential energy of a pair of particles is: (joules) 12 2 1 0 4 1 r q q U el !" = Electric Potential Energy Each ( i,j ) pair interacts: potential energy U ij ! ! < < = = j i j i ij j i ij el r q q U U 0 4 1 "# The potential energy of multiple particles is: U el > 0 for two like-sign charges ( repulsion ) U el < 0 for two unlike-sign charges ( attraction )

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Electric potential electric potential energy per unit charge q U V el = Units: J/C = V (Volt) Electric potential – often called potential Electric potential difference – often called voltage Electric Potential Volts per meter = Newtons per Coulomb
r q V 1 0 4 1 !" = r →∞ , V=0 Negative charge Positive charge V at Infinity

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Definitions: q F E ! ! = q U V el = Force = negative gradient of potential energy: dx dU F x ! = F x / q = ! d U / q ( ) dx dx dV E x ! = Electric field is the negative gradient of potential: x V E x ! ! " = y V E y ! ! " = z V E z ! ! " = Are units OK? J/(C . m)=N . m/(C . m)=N/C Electric Field and Potential