This chapter introduces the idea of electric potential and voltage.
Chap 25
The potential energy due to the electric force comes from integrating the
force over distance. Two of the most typical cases for electric forces are
-
near an infinite plane (or inside a parallel plate capacitor). The electric
field and force are constant so the potential is just force times distance
\Delta U = eE\Delta s
-
for point charges. The potential energy is
U=\frac{Kq_1q_2}{r}
. This is the potential energy
between each pair of charges. The eye often gloss over but remember this is
1/r not 1/r^2. And this is not a vector. So two important differences from
what the electric field was.
These formulas are very similar to what we had with gravity. Near the Earth
where the force of gravity is nearly constant
\Delta U_G=mg\Delta y
while in space
U_G=-\frac{Gm_1m_2}{r}
. The main difference with
electricity is the possible sign difference of the charges. The protons and
electrons move in opposite directions to decrease their energy. It is as if
some special particle would want to move up from the Earth!
Do carefully examples (before looking at solutions) 25.2, 25.3 and 25.4. Note
that when there are multiple point charges, you should not double count the energy!
Section 25.3 about the energy of a dipole is important to read but less
crucial than the rest of this chapter.
Then in section 25.4-6, we introduce the idea of potential (V) not to be
confused with potential energy U. We then apply it in more details to the two
main cases above, the capacitor, and point charge. There is an important
analogy with the concept of electric potential
| Created by Sources |
Felt by Charges |
| Electric Field |
force = q x E |
| Potential |
U = q x V |
The connection between potential and electric field will be studied more next
week. It comes, as you can guess, from the deep conceptual connection between
force and energy.
Problem solving strategy 25.1 is just energy conservation applied to our
context of electricity. Note that we will almost never have thermal energy
loss in Phys 212 since we will almost always deal with small particles moving
in vacuum where drag and friction do not matter.
Examples 25.6-25.8 are all great examples of applying conservation of energy
to electric situations.
The one thing confusing with the concept of potential (V) is the following.
Both electrons and protons always move in the direction of
decreasing
potential energy (unless external work is done on them). Because they have opposite charges, the electron move in opposite directions
but still both decrease their energy. They both move in the direction that decrease their own energy.
When we use the concept of potential, we divide by the charge. The result is that now
protons move to decrease their V, while electrons move to increase their
V
. The electrons increase their potential in order to decrease their potential
energy. (multiplying by negative charge).
We will use multiple ways to visualize the potential. I like contour map the
best and then I need to remember that electrons want to go up mountains!
Finally section 25.7 is the electric point charge of multiple charges. Like
the electric field, the electric potential can be obtained by adding the
contributions from all the charges. For a continuous distribution of charges,
this is an integral.
Integral of V are easier than the electric field because the voltage is a
scalar. There is no direction, no \hat r
.