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Electrostatic:Electric Potential

Chapter 24 Halliday-Resnick 9th Ed.

Electric potential energy: An Electric force act between two or more particles Assign an Electric Potential Energy to the system

initial ( ) final ( )Change of states

Δ = − = −Conservative force → path independent

Reference: = infinite separation → = 0 = neighboring particles → = = ΔU = −

Work done bythe force duringmove from ∞

= [J/C] (scalar)Δ = − = − = −= 0== − [volt (V)]

Electric Potential:

Work done bythe force duringmove from ∞

Calculating from

= ∙ = ∙= ∙− = − ∙= 0== − ∙

Potential due to a Point ChargeMove from to infinity∙ = cos− = − ∫ ∙; = 0; = = 1

0 − = − 1= 1 = − 1

= 1 + → +− → −

Potential due to a System ofPoint Charge

=

=== /=== ln + + /

Potential due to a continuouscharge distribution:Line of charge

Potential due to a continuouscharge distribution:charged disk =====

= + −= +

Calculating the Field from the Potential= −a positive test charge moves through adisplacement from one equipotentialsurface to the adjacent surface.the work the electric field does on the testcharge during the move is =

= −= −= −

= −

The figure shows three pairs of parallel plates with the sameseparation, and the electric potential of each plate. The electric fieldbetween the plates is uniform and perpendicular to the plates.(a) Rank the pairs according to the magnitude of the electric field

between the plates, greatest first.(b) For which pair is the electric field pointing rightward?(c) If an electron is released midway between the third pair of plates,

does it remain there, move rightward at constant speed, moveleftward at constant speed, accelerate rightward, or accelerateleftward?

2,1-33

accelerate leftward

The electric potential energy of a system of fixedpoint charges is equal to the work that must bedone by an external agent to assemble the system,bringing each charge in from an infinite distance.

Electric Potential Energy of a System of Point Charges

=

What is the electricpotential energy of thissystem of charges? Assumethat = 2 and thatql = +3 nC,q2 = -2 nCq3 = +5 nC,

Potential of a Charged IsolatedConductor

− = − ∙= 0, inside the conductor− = 0=