Download Equipotentials and Lines of Force

Experiment 2
Equipotentials and Lines of Force
The electric field lines of force are to be mapped for various configurations of electrodes.
However, because direct mapping of the electric field lines cannot be accomplished, the surfaces
on which the voltage is constant (equipotentials) will first be determined. The relationship
between equipotentials and electric fields will then be utilized in order to draw the lines of force.
Theory
When charges are moved to fixed position in space, the region in the vicinity of the
charges is altered and it is said that the chases have set up an electric field. In order to measure
the strength and direction of the electric field, a positive test charge, qo, is placed in the field and
the resulting force on the test charge is measured. The electric field strength is then


F
E  lim .
q0  0 q 0
The limit is taken to indicate that the test charge must be small enough so that it does not affect
the original charge distribution that set up the field. Notice that the direction of the field is the
same as the direction of the force on the positive test charge.
The electric field lines of force are not measured directly. The equipotentials are first
determined, then the relationship between electric fields and equipotential surfaces us used to
find the electric field lines of force; that is,
 
VB  V A    E  d s
(1)
or,
ES  
dV
,
dS
(2)
where V is the electric potential. These equations indicate that the lines of force of the electric
Fields are perpendicular to the equipotentials.
The equipotentials are surfaces on which no work is done when a charge is moved along the
surface from one point to other. A characteristic associated with the surface is that the voltage is
the same everywhere on the surface. Because voltages can be measured easily, this allows the
equipotential surfaces to be mapped. Once they are determined, the electric field lines of force
can be drawn by noting from (1) or (2) that the field and equipotential surfaces are mutually
perpendicular.
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Apparatus
o
o
o
o
equipotential and field mapper with
leads
3 sheets of conductive paper with different electrode designs
metal pushpins
DC power supply (Tri-Power Supply) with leads
VOM with leads
3 sheets of centimeter graph paper
Procedure
1)
Use four pushpins to attach the sheet of the conductive paper with point electrodes to
the corkboard.
2)
Connect the DC power supply and the VOM as shown in Figure 1.
Figure 1. The arrangement of the equipment.
3)
Turn on the DC power supply and the VOM. Set the VOM to read 20 volts. Touch the
positive electrode on the equipotential and field mapper with the moveable electrode,
and adjust the DC power supply until the voltage reading on the VOM is 8.00 volts.
4)
Move the moveable electrode to a position on the conductive sheet until the reading on
the VOM is 7 volts. Record this position on your graph paper. Locate a second
position and record. Continue in this fashion until enough points have been recorded to
allow a smooth curve to be drawn through the points. (If the 7-volt equipotential is
located too close to the fixed electrode to make an accurate determination of its
position, then start with the 6 volt equipotential.)
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5)
Repeat step (4) for 6, 5, 4, 3, 2, and 1-volt equipotentials. (If the I volt equipotential is
too close to the electrode for an accurate determination, then ignore it.)
6)
Replace e conductive sheet that has the point electrodes with the conductive sheet that
has the parallel electrodes. Repeat steps (3) through (5).
7)
Replace the sheet with parallel electrodes with a circular and straight electrode and
again repeat steps (3) though (5).
Figure 2. The other arrangements of electrodes for the other conductive sheets.
Analysis
Draw smooth curves through or close to the points on your graph that correspond to
identical voltages. These curves represent equipotential surfaces. Use a pen or pencil of a
different color and draw the lines of force of the electric field. When drawing the field lines
remember that (1) the field lines begin and end on the charged conductors, (2) the field lines are
perpendicular to the equipotentials (conductors are equipotentials also), (3) the electric field is a
vector quantity and therefore has a direction associated with it, and (4) the density of the lines is
an indication of the strength of the field.
Questions
1. Why are the electric field lines of force [perpendicular to the equipotential surfaces?
2. Why are the electric field lines of force perpendicular to the surfaces of conductors in an
electrostatic situation?
3. By examining the spacing between the equipotentials, one can get an idea of the relative
strength of the electric field at various points. What kind of equipotential spacing
indicates a strong electric field? Explain.
4. In step (9) in the Procedure section, the field lines for a hollow cylinder and plate are
found. How does the voltage inside the cylinder vary? What does this indicate about the
electric field inside the cylinder?
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