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Chapter 19

Electric Potential Energy and the

Electric Potential

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1) Electric Potential Energy

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−ΔPE = −(PEA − PEB ) = WAB

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2) Electric Potential

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ΔV =ΔPE

q0€

V =PE

q0

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3) Point Charges

If V = 0 at r = ∞, then

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V =kq

r

V

q

r

Superposition: potentials add as scalars

q1

q2

q2

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V =kq1

r1+

kq2

r2

+kq3

r3

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4) Equipotential surfaces

a) Definition

Surface with constant potential

e.g. For a point charge,

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V =kq

r= constant

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⇒ r = constant

equipotential surfaces are spheres

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e.g. parallel plates

E is uniform, and W = qEs, so

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V =−W

q= −Es = constant

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⇒ s = constant

equipotential surfaces are planes

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b) Work along an equipotential surface

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ΔV =−WAB

q= 0

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⇒ WAB = 0

Work = 0

8c) Electric field direction and equipotential surfaces

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W = Fscosθ

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W = qEscosθ

If W = 0, and E ≠ 0, then

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θ =90º €

θ

E is perpendicular to equipotential surfaces

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Electric field lines

Equipotential lines

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d) Electric field as a potential gradient

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ΔV = VB − VA =−WAB

q

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−WAB = FΔs = qEΔs

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ΔV =−qEΔs

q

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E =−ΔV

Δs

units: V/m = J/(Cm) = N/C

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In general,

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Ex =−ΔV

Δx; Ey =

−ΔV

Δy; E z =

−ΔV

Δz

Electric field points in the direction of maximum change of the potential

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rE = −∇V

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5) Biomedical examples

a) Conduction of electrical signals in neurons

V=-70mV

Resting state (selective permeability)

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Signal travels at ~ 50 m/s

Stimulated cell

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b) Medical diagnostics

- body is not an equipotential surface

- Flow of Na+, K+, Cl- ions; potential differences ~ 30 - 500 µV

- depend on stimuli and can form regular patterns

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- heartbeat (electrocardiography, ECT, EKG)

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- brain waves (electroencephalography, EEG)

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- response to light (electroretinography, ERG)