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Lecture_07

# Lecture_07 - Electric Potential Energy of Two Particles...

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q 1 q 2 r 12 ! E 1 + ! E 2 " 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: 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 1 + ! E 2 = W ext + W int + Q if ! ( mc 2 ) = 0 : Energy Principle for a multiparticle system. ! U el = " W int = " ! F int d ! l i f #

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Example An electron traveling to the right enters capacitor through a small hole at A. Electric field strength is 2x10 3 N/C. What is the change in the electron ` s potential energy in traveling from A to B? What is its change in kinetic energy? Δ ( AB)= 4mm = (1.6x10 -19 C)(2x10 3 N/C)(0.004m) =1.3x10 -18 J Δ K = . Δ U electric = -1.3x10 -18 J x ! U electric = " ! F i ! ! l = " ( " eE x ) ! x = eE x ! x
Electric potential electric potential energy per unit charge Units: J/C = V (Volt) Electric potential, V – often called potential Electric potential difference, Δ V – often called voltage Electric Potential Difference in a Uniform Field Volts per meter = Newtons per Coulomb ! U electric = q ! V , ! V = ! U electric q

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! V = " ! E i ! ! l = " ( E x ! x + E y ! y + E z ! z ) If we multiply through by q , we recover the relation between the change in potential energy and work done on q by the internal force.
30 0 ! V = " ! E

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Lecture_07 - Electric Potential Energy of Two Particles...

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