Download Electric Field and Equipotentials due to a Single Charge

Electric Field and Potential
Plotting with Phet
INTRODUCTION
When buying groceries, we are often interested in the price per pound.
Knowing this, we can determine the price for a given amount of an item.
Analogously, it is convenient to know the electric force per unit charge at points in
space due to an electric charge configuration. Knowing this, we can easily
calculate the electric force an interacting object would experience at different
locations.
The electric force per unit charge is called the electric field intensity, or simply
the electric field. By determining the electric force on a test charge at various
points in the vicinity of a charge configuration, the electric field may be "mapped"
or represented graphically by lines of force. The English scientist Michael Faraday
(1791-1867) introduced the concept of lines of force as an aid in visualizing the
magnitude and direction of an electric field.
In this experiment, the concepts of fields will be investigated and some
electric field configurations will be determined.
Background (most of which you already know)
The magnitude of the electrostatic force between two point charges q1,
and q2 is given by Coulomb's law:
Fk
q1 q2
r2
(1)
where, r, is the distance between the charges and the constant k = 9.0 x 109 Nm2/C2. The direction of the force on a charge may be determined by the law of
charges. Like charges repel, and unlike charges attract.
The magnitude E of the electric Field is defined as the electrical force per unit
charge, or E = F/q0 (N/C). By convention, the electric field is determined by
using a positive test charge q0. In the case of the electric field associated with a
single-source charge q, the magnitude of the electric field a distance r away
from the charge is
E
F kq0 q kq


q0 q0 r 2 r 2
(2)
The direction of the electric field may be determined by the law of
charges. It is in the direction of the force experienced by the positive test
charge.
The electric field vectors for several series of radial points from a positive
source charge are illustrated in Fig. 1a. Notice that the lengths (magnitudes) of
the vectors are smaller the greater the distance from the charge. (Why?)
By drawing lines through the points in the direction of the field vectors, we
form lines of force (Fig. 1b), which give a graphical representation of the electric
field. The direction of the electric field at a particular location is tangent to the
line of force through that point (Fig. 1c). The magnitudes of the electric field are
not customarily listed, only the direction of the field lines. However, the closer
together the lines of force, the stronger the field.
(a)
(b)
Figure 1
(c)
If a positive charge were released in the vicinity of a, stationary positive
source charge, it would accelerate along a line of force in the direction
indicated (away from the source charge). A negative charge would move
along the line of force in the opposite direction. Once the electric field for a
particular charge configuration is known, we tend to neglect the charge configuration itself, since the effect of the configuration is given by the field.
Since a free charge moves in an electric field by the action of the electric
force, we say that work (W = Fd) is done by the field in moving charges from
one point to another (e.g., from A to B in Fig. 1b). To move a positive charge
from B to A would require work supplied by an external force to move the
charge against the electric field (force). The work W per charge q0 in moving
the charge between two points in an electric field is called the potential difference
points:
VBA  VB  Va 
W
q0
(3)
It can be shown that the potential at a particular point a distance r from the
source charge q:
V k
q
r
(4)
If a charge is moved along a path at right angles or perpendicular to the
field lines, no work is done (W = 0), since there is no force component along the
path. Then along such a path (dashed= VB - VC = W/q0 =
0, and VC = VB. Hence, the potential is constant along paths perpendicular to
the field lines. Such paths are called equipotentials. (In three dimensions, the
path is along an equipotential surface.)
Google Phet Charges and Fields…
Electric Field and Equipotentials due to a Single Charge
(1) Click on Show E-field, Grid, and Show Numbers. Your screen should
look like:
(2) Drag a single positive charge to the center of the screen. Then place
E-field Sensors every 0.5 m to the right of the charge.
Record the distance from the charge and the E-field at that distance in
the table below:
Distance
E-field (N/C)
(3) Graph Electric Field vs distance. Does your data follow an Inverse
Square relationship?
(4) Select Clear All in the PhET Simulation and then drag a positive charge
to the center of the screen as shown. Use the equipotential plot tool
to plot the Potentials every 0.5 m as shown below.
(5) Enter your distance and potential data in the following data table:
Distance
Voltage
(6) Graph Voltage vs Distance. Is your relationship inverse?
(7) Describe the equipotential lines for a single positive charge. When an equipotential
line crosses an electric field vector, what is the angle of crossing? (One analogy
you might think about is that the equipotentials are equivalent to lines of equal
height on a hill or valley and the Electric Field arrows are the directions of steepest
ascent or descent.)
(8) Repeat Step (4) for a Negative Charge.
Electric Field and Equipotentials of a dipole and other pairs
of charges
(10) Plot Equipotentials for a positive and negative charge placed 2 m
apart as illustrated in the figure below.
Observations:
(11) Plot Equipotentials for two positive charges placed 2 m apart as
illustrated in the figure below:
Observations:
Electric Field and Equipotentials due to Parallel Lines of Opposite Charge
(analogous to a capacitor).
(12) Plot Equipotentials for two lines of opposite charges placed 3 m apart
as illustrated in the figure below:
Observations:
Write a brief conclusion elaborating on the virtual experiment and what you learned.