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Chapter 19
Electric Potential Energy and the
Electric Potential
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1) Electric Potential Energy
€
−ΔPE = −(PEA − PEB ) = WAB
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2) Electric Potential
€
ΔV =ΔPE
q0€
V =PE
q0
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3) Point Charges
If V = 0 at r = ∞, then
€
V =kq
r
V
q
r
Superposition: potentials add as scalars
q1
q2
q2
€
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,
€
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
€
⇒ s = constant
equipotential surfaces are planes
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b) Work along an equipotential surface
€
ΔV =−WAB
q= 0
€
⇒ WAB = 0
Work = 0
8c) Electric field direction and equipotential surfaces
€
W = Fscosθ
€
W = qEscosθ
If W = 0, and E ≠ 0, then
€
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
€
ΔV = VB − VA =−WAB
q
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−WAB = FΔs = qEΔs
€
ΔV =−qEΔs
q
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E =−ΔV
Δs
units: V/m = J/(Cm) = N/C
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In general,
€
Ex =−ΔV
Δx; Ey =
−ΔV
Δy; E z =
−ΔV
Δz
Electric field points in the direction of maximum change of the potential
€
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)