Transcript Slide 1

Electrical Energy and Electrical Potential
Two different things that sound alike!
Recall Work: W = F d cos(q)
In order to bring two like charges together work must be done.
In order to separate two opposite charges, work must be done.
As the monkey does + work on the positive
charge against electric force, he increases the
energy of that charge. The closer he brings it,
the more electrical potential energy it has.
This work done by external force against
electrical force is stored as electrical PE, U.
When he let it go, the charge will gain kinetic energy and can do a work.
Try the same thing with grav. force. It is the same!!!! charge → mass
So essentially, electrical potential energy of a charge is its
capacity to do the work due to its position within electric field.
Greater amount of charge → greater force needed →
greater work done → greater stored potential energy U.
In the electrical case, a charge placed in electric field will have electric potential
energy. How do we know that? If left on its own it will start accelerating due to
electric force acting on it. We say it has electric potential energy which will be
converted into kinetic energy. On the other hand if external force pushes the
charge against electric field, the work done by that force will be stored as
potential energy in the charge.
Potential energy difference between two points (∆𝑼) is equal to the
work done on a charge in order to move it from one point to the other.
DU = W
As we saw potential energy depends on the amount of charge, like the force
is dependent on the amount of charge. So the same idea that led us to
introduce electric field will lead us now to introduce ELECTRIC POTENTIAL.
Potential Difference Between Two Points (ΔV = VB – VA)
is equal to the work done per unit positive charge
in order to move it from one point to the other.
= ΔU
ΔV = W
q
q
1 𝑉𝑜𝑙𝑡 =
1 𝐽𝑜𝑢𝑙𝑒
1 𝐶𝑜𝑢𝑙𝑜𝑚𝑏
Now the same way as before with electric field,
potential difference does not depend on the charge.
• Note important difference between energy and potential:
• A point has potential, charge placed there has electric potential energy
+++++
+
+
++++
+
+
+
+ +
++++
Two points that are at the same distance from the
charged object have the same potential.
So, when two charged objects are placed
there, they are at the same potential, but the
one with more charge on it has higher electric
potential energy. It is harder to push it there.
++ +
++
Capacitor: two parallel conducting plates charged
uniformly with opposite charge
uniform electric field (the one that has
constant magnitude and direction) is
generated between two oppositely
charged parallel plates. Edge effect is
minimized when the length is long
compared to their separation.
▪ Positive charge accelerates from higher to lower
potential (from positive to negative).
▪ Negative charge accelerates from lower to higher
potential. (from negative to positive)
A ball in gravitational field accelerates.
It loses potential energy and gains kinetic energy.
◊ The work done by gravitational force is equal
to the decrease in its gravitational potential
energy which is converted into kinetic energy
Wgrav = Δ PE = ΔKE
▪
Work done by electric force on charge q
Electric force on charge q is 𝐹 = 𝑞𝐸.
It moves through a potential difference, ∆V.
The work done on it by electric force is equal to the
decrease in its electric potential energy which is
converted into kinetic energy:
W = ∆U = ½ mv2
q ∆V = ½ mv2
W = Fd = q Ed
A ball in gravitational field is pushed up by
external/applied force against gravitational field.
◊ The work done by applied force is stored as change in
gravitational potential energy in the object .
Wext = Δ PE
▪
Work done by external force on charge q
Electric force on charge q against electric field is 𝐹𝑒𝑥𝑡 = 𝑞𝐸.
It moves through a potential difference, ∆V.
The work done on it by external force against electric field is
stored in charge as the change in electric potential energy U.
W = ∆U
Fext d = q ∆V
qEd = q ∆V ⇒
𝐸 =
∆𝑉
⇒ (E) = NC-1 = Vm-1
𝑑
electron-Volt (eV)
How much work is done in moving one electron
through a potential difference of one volt?
An electron volt is the amount of energy/work it takes to
move an electron through a potential difference of 1 volt.
DU = W = q DV
1 eV = DU = W = (1.6x10-19 C) (1V)
1 eV = 1.6x10-19 J
The electron volt is not a smaller unit for volts!!!
It is a smaller unit for energy.
◊
relationship between uniform electric field E and potential
difference between two points distance d from each other along
electric field line:
ΔV = Ed
→ E = ΔV/d
and NC-1 = Vm-1
For things like batteries, we specify the potential difference between the
contacts (poles) on the batery. So a "D-cell" has a rating of 1.5 volts
which means that every 1C of charge (electrons) that moves from the
negative side of the cell to the positive side will do 1.5 Joules work.
1. Potential difference = 1.5 V →
2. Potential energy of 1 C electrons relative to positive
pole is 1.5 J.
3. That energy is being converted into kinetic energy on
the way to positive pole.
4. Kinetic energy is being converted into work due to
collisions with atoms within conductor. That is what
makes bulb (and wires unfortunately too) to heat up
and give off light (not wires, hopefuly)
5. Electrons reach positive pole completely exausted without
any energy, ready to reenergize again in the cell.
The AA-cell may only light a light bulb for 15 minutes while the D-cell may
keep the same bulb lit for several hours (simply more charge).
In the 12 volt car battery, every coulomb of charge that moves from one
side to the other does 12 Joules worth of work.
In a 120 volt electrical outlet, every Coulomb of charge does 120 Joules
worth of work as it moves from one side of the outlet to the other.
surprise, surprise ! We use the same name for different things, and even
worse we use couple of different names to express the same thing, like:
1. The variable we use for potential, potential difference, and the unit
for potential difference (volts) is V. Cute!!!!!
2. Don't let that confuse you when you see V = 1.5V
3. Electric potential energy is not the same as electrical potential.
4. The electron volt is not a smaller unit of the volt, it's a smaller unit of
the Joule.
5. Electrical potential can also be described by the terms, potential
difference, voltage, potential drop, potential rise, electromotive force,
and EMF. These terms may differ slightly in meaning depending on
the situation.