Download Today • Questions re: HW • New Concept: Electrical Potential

Voltage Notes
March 15-18
Today
• Questions re: HW
• New Concept: Electrical Potential Energy, EPE (J; eV)
• Electric Potential/Voltage, V (V)
> Near a point charge Q
> Between two Parallel Plates
Honors Physics
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Voltage Notes
March 15-18
Electrical Potential Energy, EPE (J)
When two charges Q and q are separated by a distance R, there is a
certain amount of potential energy stored in that configuration (similar to
energy stored in a spring, or the potential energy between two masses).
Q
R
q
We say that, in this case,
where k = 9 E9 Nm2/C2.
By definition, the EPE between these two charges is defined to be zero
when R = ∞. Notice that, when Q and q have the same sign, then EPE is
positive; when Q and q have opposite signs, then EPE is negative.
*This implies that, when EPE is positive, the charges want to move away
from each other; when EPE is negative, the charges want to come together.
Technically, the EPE stored in this system is defined as the work done by
an External Force AGAINST the Electrostatic Force in bringing these
two charges together from an infinite distance away.
*If there are more than two charges, you can compute the Total EPE of a
system by determining the EPE for each possible pair of charges, and then
summing the EPE's. E.g., for 3 charges...
Honors Physics
2
Voltage Notes
March 15-18
Electric Potential/Voltage, V (V)
We define Electric Potential, aka Voltage, as the EPE per unit charge; i.e.,
we define V as the ratio of EPE a charge has at a certain point to the
amount of charge itself (this is similar to how we define E as the ratio of
Force per unit charge). The key idea is that V relates to ENERGY.
Q
R
q
For the case on the previous slide, the Voltage at the location of charge q,
which is a distance R from the charge Q, would be
The idea is that, when I place a charge q at a point in space where there is
a Voltage V, that charge will then have an EPE = qV.
*Notice that the V at the location of q is INDEPENDENT of the charge q.
If Q is positive, then the Voltage would be positive; if Q is negative, the
Voltage would be negative. (This tells us simply that if we place a positive
charge q at this point, EPE is positive, and if q is negative, then EPE is
negative.)
Honors Physics
3
Voltage Notes
March 15-18
Batteries:
When you look at a battery (for example, a AAA in your calculator), it is
labeled as "1.5 V". This implies that the DIFFERENCE in Voltage
between the two terminals is 1.5 V; in turn, this means that the amount of
energy that a charge (say, an electron) will gain in moving through the
battery is EPE = qV = 1.6 E-19(1.5) = 2.4 E-19 J.
There is another unit of energy that is often used when discussing
Electricity: the Electron-Volt. 1 eV = 1.6 E-19 J; it is the amount of energy
that a proton/electron will gain when it moves through a voltage of 1 V.
Thus, in the above example, the electrons would have an energy of 1.5 eV.
Honors Physics
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Voltage Notes
March 15-18
Example 1: What is the Electric Potential a distance of 0.25 m from a Van
de Graaff generator if it has a net charge of -8 E-6 C?
Example 2: A carbon nucleus has 6 protons and 6 neutrons. What is the
Voltage a distance of 3 E-12 m from this nucleus?
*Example 3: What is the Electric Potential difference between points A
and B (∆V = VA - VB) in the diagram below? Assume Q = 4 E-6 C.
1m
3m
Q
Honors Physics
A
B
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Voltage Notes
March 15-18
Relationship between V and E:
In a region where the Electric Field is Uniform, if a charge q moves over a
distance d, it will experience a change in Electric Potential such that
*We must understand going forward that it is only the difference in Voltage
that matters as far as charges are concerned (similar to how only changes in
potential energy are truly meaningful). Often we will choose either our
"initial" or "final" Voltage as zero, and hence we will often conclude that
V = Ed
The Voltage "difference"
In the diagram to the left, assume there is a
uniform Electric Field E that is directed
downwards, and the distance from top to bottom
is d. A charge +q placed near the top "plate" will
feel a force directed downwards; its EPE at that
point would be positive, and it would have a
tendency to move downwards.
between the top and the
bottom, V = Ed. By the definition of V, this V = EPE/q; in other words, the
EPE = qV = qEd.
Compare this to the following:
In the diagram to the right, a mass m is
placed in a uniform gravitational field g
that is directed downwards. When released
from rest, the mass feels a force directed
downwards; its PEg at this point would be The difference in potential
energy from the top to the
positive, and as a result it would have a
bottom is ∆PEg = mgh.
tendency to move downwards.
Honors Physics
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Voltage Notes
Honors Physics
March 15-18
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