Physics of Energy and Voltage
ECE 3030 Physical Foundations of Computer Engineering
Dr. Vincent John Mooney III
Associate Professor, School of Electrical and Computer Engineering
Adjunct Associate Professor, School of Computer Science
Georgia Institute of Technology
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Some Early History
• 600 BC, Thales of Miletus would rub amber (a type of stone which
originates from tree resin) and attract straws & feathers
• Greek word for amber is elektron
• William Gilbert, physician to Elizabeth I (1533-1603), showed similar
effects with a variety of materials now known to be insulators
• In the 1700s a lot of similar experiments were carried out
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Some Early History (continued)
• Ben Franklin published Experiments and Observations on Electricity in 1748
• defined positive flow as what we now know to be flow of electrons
• induction (magnets)
• conduction
• In the early 1900s J. J. Thompson showed that there exist particles (now
called electrons) common to all atoms with a unique ratio of charge to mass
• In 1909 R. A. Milliken showed all electrons carry the same charge, -|q|
• Today we know of more than 100 elementary particles with charge -q, 0 or q
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Coulumb
• In 1785 Charles Augustin de Coulumb made the first recorded
measurement of charge
• ଵଶ =
௤ ௤
భమ మ ௥
௥భమ
|q|=1.6022 x
• permittivity of free space ε଴ =
• ⇒ଵଶ =
10-19
ଵ
ସπ௞
C
k = 8.98755 x
= 8.85419 x
ே·௠మ
9
10
஼మ
஼మ
-12
10
ே·௠మ
ଵ
௤భ ௤మ
௥
మ ସπεబ ௥భమ
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A battery or a portion of Silicon has voltage
V = 5 Volts: what does this mean?
• Mechanical theory of work
• work = force * distance ( W = F*s )
• units: Newtons * meters = Joules = (kg*m2)/s2
• James Prescott Joule (1818-1889) was an English physicist who contributed greatly to our understanding of the
concepts of work and energy
• Consider Newton’s second law, force = mass * acceleration
• =
ௗ ଶ௫
ௗ௧ଶ
=
ௗ௩
ௗ௧
ௗ௩
ௗ௧
ௗ௫
=
ௗ௧ ଵ
• ⇒ = = =
•
஻
⇒ ஺ =
௩
௩ ಳ ಲ
ଵ
= ஻ଶ − ஺ଶ = (→
)= change in kinetic energy ଶ
ଶ
ଶ
• Energy is also measured in Joules
• Mechanically, an object acquires potential energy U(x) when it is lifted
• e.g., lift a block vertically, Wg = -Ug where the subscript “g” indicates due to gravity
ௗ௎(௫)
• Considering only the direction x, = −
ௗ௫
• Law of energy conservation for mechanical systems
ଵ
ଶ
ଵ
ଶ
௫
• ஻ + ஻ଶ = ஺ + ஺ଶ + ௫ ಳ where f is due to friction
ಲ
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Electromagnetic Force
• Force (in Newtons) between two point charges q0 and Q
• ଵଶ =
ଵ ௤బ ொ
௥
మ ସ஠εబ ௥మభ
• ε଴ = permittivity of free space = 8.85419 x
஼మ
-12
10
ே·௠మ
• How strong is the electric field
ࡲ
ଵ
ொ
ே
• = lim
=
௥ = Newtons per Coulomb =
మ ସ஠εబ ௥మభ
஼
(௤బ →଴) ௤బ
• Q’s force on q is () = ()
• Note that if Q is positive, then E is directed radially outwards; if Q is
negative, the opposite is the case and F has a negative value.
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Work Done by the Electric Field due to Q
• dW = F * dr
• ⇒஺஻ =
௤బ ொ ଵ
(
ସ஠εబ ௥ಲ
−
ଵ
)
௥ಳ
in units of Newtons * meters
• Note that the work done by the electric force field over any closed path
is zero
஻
• ⇒ we can define a potential function U(r) such that ஺஻ = ஺ ()
௤ொ ଵ
• for two point charges q and Q, we find =
where r is dist. from q
ସ஠εబ ௥
and Q
• if, instead of point charge Q, we have a continuous distribution with charge
density ρ
௤
ௗொ
௤
ௗ௩
• ܷ ࢘ =
= ସ஠ε ‫׬‬௏ ρ ௥ where V is the volume of the charged material, rc is
‫׬‬
ସ஠εబ ௏ ௥೎
బ
೎
the distance from q to the differential charge element dQ = ρ dv, and U(r) has units
Joules/Coulomb
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Electrostatic Potential
• We define electrostatic potential V(r) as follows:
• () = lim
(௤బ →଴)
௎(࢘)
௤బ
=
ଵ
ସ஠εబ ௏
ρ
ௗ௩
௥೎
௃
஼
= Joules per Coulomb = = Volts
• Rearranging the units of the electric field
• = Newtons per Coulomb =
ே
஼
=
௃
௠·஼
=
௏
௠
= Volts per meter
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