Electric Potential & Voltage
► Objectives/Syllabus
Refs:
 9.3.1: Define electric potential and electric potential
energy.
 9.3.2: State and apply the expression for electric
potential due to a point charge
 9.3.3: State and apply the formula relating electric field
strength to electric potential gradient.
 9.3.4: Determine the potential due to one or more point
charges.
 9.3.5: Describe and sketch the pattern of equipotential
surfaces due to one and two point charges.
 9.3.6: State the relation between equipotential surfaces
and electric field lines.
Work and Potential Energy
►Potential
energy is energy of position
 Relative to measuring point
 Ground or infinity
►Work
(fs)
fs) done on an object changes
its potential and/or kinetic energy
Electric Potential Energy
►Work
is done to move a charge
through an electric field, so electric
potential energy is changed.
Electric Potential Difference
(Voltage)
►Electric
potential = potential
energy/charge
►ΔV = W/q so ΔV = ΔEp/q
►Vq = ½ mv2 (Data Book: Ve = …)
►Scalar Quantity
►1 Volt = 1 Joule/Coulomb
1
More with Potential
Equipotential lines
•Electric Field Applet
►Using
calculus you can show that
the work to move a charge from
infinity to point p = -kQq/r so…
►V = kq/r = q/(4πε
q/(4πε0r)
Some typical Voltages
Lightning
108 V
High-voltage power line
106 V
TV tube
104 V
Household Outlet
110 V
Resting potential across nerve
membrane
10-1 V
Voltage and Electric Fields
►W
= qV and W = Fd = qEd
 So qV = qEd
► So
E = V/d (in a uniform field)
► More
generally:
 E = - ΔV / Δx (in Data book)
 This would be the slope of a V vs. x graph
(derivative with calculus)
Gravity vs. Electricity
The electronvolt (eV)
eV)
►A
unit of energy
► Joules are too large for many subatomic
applications
► 1 eV = the amount of energy gained by one
electron moving through 1 Volt of potential
difference
► 1 eV = 1.6 x 10-19 J
Gravitation
Electricity
Acts on
Mass (+ only)
Charge (+ or -)
Force
F = Gm1m2/r2
attract only
Relative Strength
1
F = kq1q2/r2
attract or repel
1042
Field
G = G M/r2
E = kQ/r2
Potential
V = -GM/r
V = kQ/r
Work Done
Independent of
path
U = -GMm/r
Independent of
path
U = kQq/r
Potential energy
Note
K = 1/(4π
1/(4πε0)
2