Download Electric Potential Energy v2

ELECTRIC POTENTIAL ENERGY
ELECTRIC ENERGY
Since the fields are similar between gravitational and electric
energy; both are inversed squared force fields
This represents the amount of energy to bring the charge to a
radius of infinity (if repulsion) or 0 (if attraction)
We can use a similar relationship for energy:
𝐸𝐸 =
𝑘𝑞1 𝑞2
𝑟
𝐸𝑔 =
𝐺𝑀𝑚
𝑟
Include sign of charge, negative value indicate attraction, positive value
indicate repulsion
ELECTRIC POTENTIAL (V)
Value of potential energy per unit positive charge
Represents work required to move a positive
charge at rest at infinity to at rest at another
point in the field
Attractive - Energy required to remove to stop (-)
Repulsive – Energy required to pull in in from ∞ (+)
𝑉=
𝐸𝐸
𝑞
𝑜𝑟 𝑉 =
𝑘𝑞1
𝑟
or 𝐸𝐸 =qV
Units: J/C
At r=o, Energy is large positive value
Very close, lot’s of stored energy because it
is ready to be pushed away with a lot of
force
At r= infinity, energy is small positive
value, very little potential to be pushed
At r=o, Energy is large negative value
Very close, requires lot’s of external energy
to be pushed away to infinity
At r= infinity, energy is small negative
value, very little energy required to be
pushed further away
VOLTAGE IS….
Energy per unit charge (per coulomb)
You can create the analogy…
It is Energy per electron
ELECTRIC POTENTIAL DIFFERENCE (∆V)
Work (change in energy) required to move a charge from
one point to another in an electric field
Current (flow of charge) redirects charge until electric
potential reaches zero
 Current flows downhill
Electron flow is from negative to positive
BATTERY
• The battery maintains a potential
difference
• A charge escalator - maintains a
charge separation
• An electric field is created inside the wire
• The electric field strength applies a force
on the electrons which generates a current
• Moves from a higher potential to a lower
potential (- to +)
• FMI : http://www.phy-astr.gsu.edu/cymbalyuk/Lecture16.pdf
DERIVE ∈=
∆𝑉
𝑑
This equation only applies for a constant electric field as
seen between two parallel plates
Only a constant electric field because of the evenly spread
electric charge over the plate, the field within is changed from an
inverse squared force field to a linear squared force field
 Derivation for a infinite line wire: http://faculty.wwu.edu/vawter/PhysicsNet/Topics/ElectricForce/LineChargeDer.html
Since there is an attractive and repulsive field and there is a
linear relationship, the sum of the attractive and repulsive forces
are a constant
DERIVE ∆𝑉 =
1
𝑘𝑞(
𝑟𝐵
−
1
)
𝑟𝐴
Applies for a point charge in an electric field
NOTE
W = ∆Ee
Work can also be used to produce kinetic
energy as ∆Ee=∆Ek
EXAMPLE
Calculate the electric potential at a distance
of 0.80m from a spherical point charge of
+8.9µC.
Ans: V = +1.0 x 105 V
EXAMPLE
Find the plate separation for two parallel
plates that have an electric potential
difference of 120V and produces an electric
field of 960N/C.
Ans: r = 0.125m
EXAMPLE
How much work is done to increase the potential of
a charge of 15µC with 120V?
Ans: W = 1.8 x 10-3J
EXAMPLE
Two spheres are located 0.80m from each other. Sphere
X has a charge of -8.1 x 10-4C but sphere Y has a charge
of -1.68 x 10-4C and is free to move. Both spheres have a
mass of 1.0 x 10-2 kg. How fast is sphere Y moving when
it is 1.5m from sphere X?
Ans: 3.8 x 102 m/s