Transcript Path of Least Time - Rutgers University

Electrostatics
Quantities & Concepts
Charge (charge conservation)
Electrostatic Potential Energy
Electrostatic Force
Electrostatic Potential
Electric Field
Electric Field Lines
Electric Flux
Gauss’ Law
◦ Potential
◦ Voltage
◦ Electromotive Force (EMF)
Charge
Electrostatic Force
Coulombs Law
-
+
+
“sames” repel
+
“opposites” attract
Electric Field
Coulombs Law
The “field point” is a location of the
“system” (aka, “the object of interest”).
The “surroundings” creates “electric
field” and the system (to be located at
the field point) feels the effect
+
Charge in the “surroundings” is
associated with the “electric field”
(the surrounding charge creates
the electric field)
Electric Field Lines
+
“Electric Field Lines” are a
visual pattern generated by
considering the force a
“positive test charge” would
feel if placed at various
locations.
Electric Flux
“Electric Flux” is electric field
times area (but only the field
component perpendicular to
the area.
If the area is a closed surface
then flux is positive if field is
leaving the enclosed volume.
Flux is negative if the field is
entering the enclosed volume.
Gauss’ Law
𝑞′
Φ=
𝜖0
q‘ is the charge inside the
closed surface
The total electric flux for a
closed surface is proportional
to the charge enclosed.
Gauss’ Law Examples
Point Charge and charge
distributions with spherical
symmetry.
Infinite “sheet” of charge
𝜎
𝐸=
2𝜖0
+
Parallel Plate Capacitor
𝜎
𝐸=
𝜖0
𝑘 𝑞′
𝐸= 2
𝑅
q’ is charge inside your radius
σ is charge density
+
−
on positive plate
Potential Energy & Potential
final
𝑞
initial
Δ𝑈
Δ𝑉 =
𝑞
System is moved from initial to final.
Electrostatic force does work. This work
is “conservative” so we can define
“potential energy”, Δ𝑈 = −𝑊 = +𝑊𝑎𝑔𝑒𝑛𝑡
“potential” is potential energy divided by
system charge. Joules per coulomb is volts
Potential for point source charge
Coulombs Law
R
q
𝑘𝑞
𝐸= 2
𝑅
𝑘𝑞
𝑉=
𝑅
Potential for uniform field
V1
V2
E
E is constant
High
Volts
Low
Volts
d
Δ𝑉
𝐸=
𝑑
Electric field goes from high to low volts.
A newton per coulomb is a volt per meter.