Download Electric Potential

Electric Potential
When going for a hike there are two things to consider.
Chapter 16
1. How high up are you going? (What is
your change in elevation?)
2. How much energy will it take to get
there? (How much potential energy
will you have once you get there?)
Which hiker is doing more work to get to the top of
the mountain? (which hiker will have more potential
energy when at the top?)
Even though they are climbing the same mountain the
hiker with the heavier (more massive) load will be doing
more work (or will have more potential energy at the top)
If the hiker trips, his potential energy will convert into
kinetic energy and he will fall down the hill.
Just like hikers, charges can have potential
energy too. That is called ELECTRIC potential
energy.
Electric Potential &
Electric Potential Energy
Work Done on the Ball
Energy (Potential) Gained
Kinetic Energy
Work Done equals Energy Gained
Electric potential energy has to do with where
the object is (V) (compared to where it wants to
be) and how much charge it has (Q).
PEE = QV
GRAVITATIONAL potential energy has to do
with where the hiker is (y) (how high up are
they) and how hard gravity pulls on them (mg)
(how heavy their pack is).
PEg = mgy
1
Electric Potential Energy
The sign of the charge
in thisamount
case matters
Defined as the actual
of !
energy a charge has as a result of its
being acted upon by an electric field.
In general, no one really talks about how much work
someone did climbing a mountain or how much potential
energy they had once they got there. Instead
everyone talks about the elevation of the peak.
The same is true for
charged objects.
PEelectric = QV
We are usually interested in
potential energy difference, or the
change of potential energy
would be similar to
Electric Potential This
defining height as the
potential energy per
unit weight.
Defined as the electric potential
energy per unit charge. For a point
charge, or spherical charge, the
potential is given by the formula…
V=
kQ
d
Potential has units of
energy/charge
Joules/Coulomb = Volts
Electric Potential
describes properties of a
point in space as the
result of being in the
proximity of a charge.
Just as height describes
properties of a point in
space as the result of
being in the proximity of
a gravitational field.
Q
A brief Recap:
•The electric field describes what an object in the
proximity of a charge is feeling regardless of the
amount of charge on the object.
•The electric potential describes where an object in
the proximity of a charge IS compared to where the
object wants to be regardless of the amount of
charge.
•The height describes where an object is in the
proximity of another mass compared to where the
object wants to be, regardless of the amount of
mass.
Charges move to decrease
their potential ENERGY
Masses will always try to move to lower their
potential energy. (This is why meatballs roll off the
table and onto the floor…)
Charges will always move to lower their potential
and thus their potential energy. But it gets a bit
trickier
High PE
Low PE
+34 J
-34 J
2
PE = QV
-
Positive charges want
to be close to
-2.3V
negative charges
+Q x -V = - PE
-28.2V
8.8V
1) 1/3
2) 1/9
3) 3
4) 9
5) zero
+
-9.7V
1.7V
If the distance from a negative 3C charge is tripled,
the electric potential changes by a factor of…
-5.7V
Negative charges want
to be close to
positive charges
-Q x +V = - PE
If the distance from a negative 3C charge is tripled, the
electric potential changes by a factor of…
1) 1/3
2) 1/9
3) 3
4) 9
5) zero
You will NOT confuse
Electric Potential with
Electric Potential Energy!
Two point charges of +3.4μC and +6.6 μC (10-6)
respectively, are separated by 0.20m. What is
the potential energy of this 2 charge system?
Another equation for electric
potential energy (wait for it…)
PEelectric = QV
PE =
1) +0.34J
5) +5.2J
kQ
V=
d
2) -0.75J
3) +1.0J
4) -3.4J
kQ1Q2
d
Q
3
Two point charges of +3.4 and +6.6
microcoulumbs (μC, 10-6) respectively, are separated
by 0.20m. What is the potential energy of this 2
charge system?
1) +0.34J
5) +5.2J
PE =
2) -0.75J
kQ1Q2
d
=
3) +1.0J
When going hiking, it is helpful to bring a map.
Hikers use topographical maps.
4) -3.4J
(9 × 109 )(3.4 ×10−6 )(6.6 ×10−6 )
0.20
PE = 1.01 Joules
Electric Potential due to a Point Charge
Equipotential Lines & Electric Field Lines
+ + + + + +
+
The Electric Potential Produced by a
Heart Beat
The lamp will not glow when it is held with both
ends equidistant from the charged Van de Graaff
generator. But when one end is closer to the dome
than the other, a current is established and it glows.
Why?
4
Consider equal potential lines
Consider equal potential lines
Consider equal potential lines
Hmmm…Now the
ends are at a
different
potential
It’s all about the chemicals
Hmmm…the ends
are at the same
potential
Why does anyone care
about electric potential?
Why do they react?
All elements strive to have 8 valence electrons.
What happens when two chemicals are mixed together?
sodium
+
water
=
2
# of Valence electrons
1
2
3 4 5 6 7 8
They React!
5
Some elements do this by giving away valence electrons
K -> K+ + eSome elements do this by gaining valance electrons
Batteries harness this flow of electrons.
In a battery, elements are placed close to each other,
without touching, so they do not react.
S + 2e- -> S2When a potassium atom (K) is placed next to a sulfur
atom (S), they react and electrons flow from the
potassium atom to the sulfur atom.
A wire connects the two elements.
The wire allows the transfer of electrons from one
element to the other.
This means, there must be an electric potential
difference between potassium & sulfur.
This movement of electrons generates ELECTRICITY!
Rechargeable batteries
Rechargeable batteries can be “reset”
A dead rechargeable battery can be plugged into the
wall.
As the zinc (Zn) looses
electrons, it goes from solid
zinc into an ion dissolved in
water.
As the dissolved hydrogen
ions (H+) gains electrons,
they become hydrogen gas
and leave the container.
Eventually the chemicals run out, and the battery is
considered dead.
r V
E=
d
The electric potential (voltage) from the WALL returns
the electrons and chemicals to their original starting
position to be used again.
This process is not perfect so rechargeable batteries
eventually die as well.
Consider two parallel conducting plates.
There exists between them a uniform
Electric Field.
V
Actually, the field is uniform
only if…
1. You are not near one of the
edges.
2. The size of the plates is
large compared to the
separation.
d
6
At which location will the electric field
between two charged parallel metal plates be the
strongest in magnitude?
Consider a positive charge between
the plates…
1) Near the positive plate
+
+
+
+Force
+
+
+
2) Near the negative plate
+
3) Midway between the two plates
4) It’s actually constant throughout the
space between the plates.
+
r- V
E=
V
d
F =Q
r - - rF = QE r
-
-
+
1
3
2
-
d
At which location will the electric field
between two charged parallel metal plates be the
strongest in magnitude?
1) Near the positive plate
2) Near the negative plate
+
-
V
3) Midway between the two plates
4) It’s actually constant throughout the
space between the plates.
V
V
+ + ++
- --- -
-----
+ + + +
7
V
Electrostatic Equations:
Force
Electric Field
Electric
Potential
Electric Pot.
Energy
F unit: N
E unit: N/C
V unit: V
kQ
V=
d
PE unit: J
kQ Q
F = 12 2
d
kQ
E= 2
d
F = EQ
QV
F=
*
d
PE =
kQ1Q 2
d
PE = QV
V
E=
d
*
PE = QEd *
•Parallel plate equations: d = distance between plates
8