Download Electric Potential

Electric Potential
Note that potential and potential energy are different things.
In a uniform gravitational field the change in gravitational potential associated with
moving a distance r is given by:
Vg  g y , where y  r sin  represents distance moved vertically (up is positive).
By analogy, write down the equivalent expression to represent the change in electric
potential associated with moving a distance r in a uniform electric field:
VE  ________, where r sin  represents the distance moved ____________________.
V is known as “potential difference”, and is also often referred to as “voltage.”
Potential difference is a lot like pressure. If there is a potential difference between two
points then there is a tendency for charges to move from one point to another.
Positive charges move toward lower potential (and lower potential energy).
Negative charges move toward higher potential (this is also lower potential energy).
Equipotentials: An equipotential line, or an equipotential surface, connects all points that
have the same potential. What do the gravitational equipotential surfaces look like in this
room?
Equipotentials are always perpendicular to field lines. In fact, field lines point in the
direction of the maximum decrease in potential.
Two charges, +3Q and –Q, are separated by 4 cm. Are there any points along the line
passing through them (and a finite distance from the charges) where the net electric
potential is zero? If so, where?
Are there points off the line, near the charges, where the net electric potential is zero?
Consider the following two-dimensional situation. You place four charges in a square,
with one charge at each corner. Each charge has a magnitude of Q, but you get to choose
whether it is + or –. Each charge is a distance r from the center of the square.
How many different arrangements of four charges are there?
How many different values can you obtain for the electric potential at the center of the
square?
Figure out how many of the various arrangements of charges correspond to each of the
possible values of the electric potential at the center, and draw some sketches to go with
them.
More Potential, and Capacitors
Note that potential and potential energy are different things.
Two charges, +3Q and –Q, are separated by 4 cm. The charges are on the x-axis, with the
+3Q charge at x = -2 cm and the –Q charge at x = +2 cm.
Ask a question involving force for this situation.
Ask a question involving field for this situation.
Ask a question involving field, and then a follow-up question involving force.
Ask a question involving potential energy for this situation. Then re-phrase the question
without using the word “potential” or the word “energy”.
Ask a question involving potential for this situation.
Ask a question involving potential, and then a follow-up question involving potential
energy.
A capacitor is a device for storing charge. A common example is a parallel-plate
capacitor, which consists of two metal plates placed parallel to one another. The plates
can be separated by air, vacuum, or an insulating material – a piece of insulating material
in a capacitor is known as a dielectric. List any practical applications of capacitors that
you are aware of.
There are four basic equations we use for capacitors:
1. C V  Q : The charge Q stored on a capacitor is proportional to V , the potential
difference across the capacitor. C is the capacitance of the capacitor, which has units of
farads (F).
2. Capacitance is a measure of how much charge a capacitor can store. It is determined
solely by the geometry of the capacitor, and whether anything is between the capacitor
 A
plates. For a parallel-plate capacitor the capacitance is given by: C  0 .
d
A is the area of each plate; d is the distance between the plates;  is the dielectric
constant, which is equal to 1 for vacuum and almost exactly 1 for air.  0 is the
0 
permittivity of free space, and it is related to k.
1
2
1
4 k
1
2
 8.85 1012 C2 / N m2
3. Energy stored in a capacitor is given by U  C  V   Q V 
2
1 Q2
.
2 C
4. We assume that parallel-plate capacitors have a uniform electric field, so the
relationship between the electric field inside a capacitor and the potential difference
across the capacitor is V  E d .
Capacitor problems are generally split into two kinds:
1. The capacitor is always connected to a battery or power supply that has a fixed
potential difference. This ensures that the _________________________ is constant.
When you make a change to the plate separation, dielectric constant, or plate area (that’s
hardest to change) that changes the __________________________. Knowing what is
going on with those two variables allows you to calculate
____________________________________________.
2. The capacitor is charged by first being connected to a battery or power supply,
and then disconnected so it is isolated from everything. This ensures that the
_________________________ is constant. When you make a change to the plate
separation, dielectric constant, or plate area (that’s hardest to change) that changes the
__________________________. Knowing what is going on with those two variables
allows you to calculate ____________________________________________.
More Capacitors
Consider the situation of a parallel-plate capacitor. First, assume the plates are far apart.
Connecting the capacitor to a battery causes, in effect, electrons to be pumped from one
plate of the capacitor to the other. This gives a charge of –Q on one plate and +Q on the
other, so we say that the capacitor stores a charge Q.
The “electric pressure” the battery is working against is the repulsion of all the like
charges on each plate. A particular battery can basically achieve a particular charge
density on the plates, and then no more charge can be pumped.
If we increase the area of the capacitor plates do you think more charge can be stored on
the capacitor, or less? Why?
If we now bring the capacitor plates close together the positive charge on one plate, and
the negative charge on the other, experiences some attraction because of all this opposite
charge in its vicinity. More charge can be stored on the plates in this case because the
battery does not have to do everything itself – it gets some help from the charge on the
other plate.
Sketch the electric field between the plates of a capacitor.
Usually we fill the space between the capacitor plates with insulating material, which we
call dielectric material. The dielectric material gets polarized by the field in the capacitor,
but the dielectric material does not allow charge to flow from one plate to the other.
Sketch the electric field in the capacitor when the dielectric material is present.
Now introduce a rectangular piece of metal between the plates (it can’t touch either
plate!). Draw the field again.
Can you see any disadvantages in using metal between the plates?