Download Chapter 2 Motion Along a Straight Line Position, Displacement

The contour lines show points on the mountain that are
atElectric
the same elevation.
Potential, Energy, Capacitance
The yellow
contour
line connects points
that are
16-2
Equipotential
Surfaces
14,200 feet above sea level.
Since
myus
weight
180
when I am map:
standing on that
Most of
have is
seen
a lbs,
topographical
contour line I have a potential energy of
UG = mgh = (180)(14200) = 2,556,000 ft•lbs
FYI: If the altitude of Milwaukee is 600 ft, my potential energy in
Milwaukee is U = (180)(600) = 108,000 ft•lbs, making U = 2,448,000
ft•lbs. Where did this energy come from?
T or F: The gravitational field vector g is perpendicular to every point on
the contour line.
Topic 6.2 Extended
E – Equipotential surfaces
The 2D contour lines
define a 3D surface:
Here's the 3D view from
the top of Mount Elbert:
Electric Potential, Energy, Capacitance
16-2 Equipotential Surfaces
It is easier to visualize how these equipotential
surfaces fit together to form a 3D image of the
actual surface if we concentrate on the vicinity of
the crest of Mount Elbert:
Let's look at the equipotential surfaces from 14,200 feet
up to the top of Mount Elbert:
14400
14360
14320
14280
14240
14200
Rotation, tilting, and stacking of these equipotential
surfaces will produce what appears to be a 3D image of
Mount Elbert:
Rotation, tilting, and stacking of these equipotential
surfaces will produce what appears to be a 3D image of
Mount Elbert:
Topic 6.2 Extended
E – Equipotential surfaces
Of course, on the planetary
scale the equipotential
surfaces will be spherical,
not flat.
And the contour lines
will look like this:
g
g
g
T or F: The gravitational field vector g is perpendicular to every point on
the contour line.
Question: Why are the surfaces farther from the center farther apart?
Topic 6.2 Extended
E – Equipotential surfaces
The negative point charge
acts as a planet, setting
up equipotential surfaces
in the same way:
And the contour lines
about a negative point
charge will look like
this:
E
E
E
T or F: The electric field vector E is perpendicular to every point on the
equipotential surface.
Question: Why are the surfaces farther from the center farther apart?
Topic 6.2 Extended
E – Equipotential surfaces
Suppose we have two parallel plates separated by 15 mm
and charged by a 9 V battery.
(a) How far apart would the equipotential surfaces be
between the plates, if their potential difference was
to be 0.10 V?
Since the electric field is constant
between the plates the equipotential
surfaces will be evenly spaced (unlike
+
those around a point charge).
+
V = Ed
first we find the
+
9 = E(0.015)
value of the electric
+
field...
+
E = 600 V/m
+
V = Ex
now we find the
+
distance x
0.10 = 600(x)
+
between the
x = 1.6710-4 m
+
surfaces...
+
0.015 m
Topic 6.2 Extended
E – Equipotential surfaces
Suppose we have two parallel plates separated by 15 mm
and charged by a 9 V battery.
(b) If we assign the value of 0 V to the negative
plate, where is the equipotential surface with a
potential of +3.75 V located?
We can use the formula V = Ex:
0.00625 m
3.75 = 600x:
x = 0.00625 m
-
+
+
+
+
+
+
+
+
+
+
0.015 m
Topic 6.2 Extended
E – Equipotential surfaces
If we know the potentials and the
geometry of the equipotential surfaces
surrounding a charged object we can find
the value of the E-field using
V
Electric Field
E = x
From Potential
For example, suppose we are given
that the voltage difference between
the negative plate and the red
equipotential surface is 3.75 V (it
is) then the above formula gives us
V = - V - V0
E = x - x0
x
3.75 - 0
= .00625 - 0
= -600 V/m
0.00625 m
-
+
+
+
+
+
+
+
+
+
+
0.015 m
this is the expected value
FYI: The negative in the above formula gives the correct direction of E.
FYI: If you are given Topic
the equipotential
you can construct the E6.2 surfaces,
Extended
field lines.
E – Equipotential surfaces
Sketch in the equipotential surfaces between the two
charges.
+
-
FYI: The definition ofTopic
the eV uses
an electron.
But any particle that has a
6.2
Extended
charge which is an integral number can use electron volts as an energy
E – Equipotential surfaces
quantity.
THE
VOLT
eVNOT an SI unit of energy, but it is used often for
FYI:ELECTRON
The electron
volt is
describing
Recall the
relationship
between
voltage (electric
the energy
of atomic-sized
particles.
potential) and potential energy: U = qV.
If we place an charge in an electric field, it will
accelerate, changing its kinetic energy.
From energy considerations we have
K + U = 0
K = -U
K = -qV
The Kinetic Energy
Change of a Charge
We define the electron volt (eV) as the kinetic
energy gained by an electron accelerated through a
potential difference of exactly 1 volt:
K = -qV
1 eV = -(-1.610-19 C)(1.000 V)
1 eV = 1.610-19 J
Electron Volt