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Objectives:__

1. To learn the concepts of electric field lines and equipotentials,

2. To experimentally search points, in an electric field, having the same potential (equipotential lines), and

3. To use the equipotential lines for drawing the electric field lines.

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Equipment:__

A cork board, four tacks, Ag-preparation solution 200, a small and pointed paintbrush, a voltmeter, a few sheets of conducting paper, a dc power source, and connecting wires.

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__Theory:__

Electric field lines around a positive point charge are
directed radially outward. The reason is the fact that **test charge **is defined
as **a small positive charge**. When test charges are placed around a positive charge, they
will be repelled and move radially outward. On the contrary, when test charges
are placed around a negative charge, they will be pulled radially inward. The
field lines for a single positive and a single negative point charge **when
each acts alone** are shown in the following figure:

Fig. 1

Equipotential surfaces are necessarily spheres centered at
the point charge. At any point on an equipotential surface (or sphere around a
single point charge), the potential is the same. That is the reason for the
choice of word “equipotential.” In two dimensions (on paper), equipotential
surfaces become equipotential lines (for example, spheres become circles). It
is important to note that any radial line (field line) is perpendicular to all
equipotential surfaces (spheres) around a point charge. It can be shown both
mathematically and conceptually that regardless of the type of charge
distribution (whether single point charge, two point charges, a dipole, or any
form of charge distribution), **field lines are always perpendicular to
equipotential lines. This concept may be used to draw field lines around any
type of charge distribution if equipotential lines are first determined.**

Fig. 2

The field lines and equipotential lines around an **
electric dipole** are shown below**:**

Fig. 3

The field lines and equipotential lines around a charge
distribution similar to that of a parallel-plate capacitor are shown below**:**

Fig. 4

Equipotential lines can be found experimentally by using a
voltmeter and finding points around a certain charge distribution that are at
the **same** voltage (electric potential). When these points are determined
and marked, they may be connected to form the equipotential lines. Field lines
can then be drawn perpendicular to the equipotential lines.

The types of charge distribution that will be used in this experiment are:

Fig. 5 (a) Fig. 5 (b)

a) two equal and opposite point charges (an electric dipole), and

b) two equal and opposite parallel line charges (similar to a parallel-plate capacitor).

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Procedure:__

1) Use the Ag-200 silver solution and a thin brush to draw the above-mentioned two types of charge distributions on the conducting paper as shown below:

1) Place the conducting paper shown in Fig. 5(a) on the corkboard with a few sheets of regular size white paper underneath.

2) Press two metallic tacks into the center of the silver spots and into the corkboard.

3) Connect the dc power supply to the tacks with appropriate wires.

4) Set the power supply to an appropriate voltage so that the voltmeter shows enough sensitivity on the conducting paper.

5)
Place one terminal of the voltmeter at point A (**Fig. 5a**), and with
its other terminal search for points on the conducting paper that are
equipotential with point A. At any of these points, the voltmeter should read
zero. Locate a number of points that are about or at most 1 inch apart. Make a
hole where each point is found by pressing a** tack **through the paper(s)
into the corkboard.

6)
Due to symmetry, you will find that all points equipotential with A fall
along the dotted line as shown in **Fig. 5a**. In other words, the
equipotential line through point A (selected on the perpendicular bisector of
the line connecting the charges) is a straight line. However, the
equipotentials through points B, C, D, and E will be curved lines.

7) Repeat steps 6 and 7 for each of points B,C,D, and E. For any of these points you will find a curved equipotential line.

8) Turn off the power, disconnect the voltmeter, and remove the tacks placed at the silver spots. Each student must obtain one sheet of white paper placed underneath the conducting paper with holes in it.

**To each member of the
group:**

9) Circle the location of each charge and mark it as (+) or (-). The holes forming each curve must then be connected by a pencil in an artistic way such that a nice curve is obtained and not a zigzag line. This means that the line that best fits the points (holes) must be drawn, even if the line (curve) does not exactly pass through each point.

10)
Once all equipotential lines are drawn, the field lines can be drawn
keeping in mind that anywhere a field line crosses an equipotential line the
angle must be 90˚. Choose a point on one of the equipotential lines and draw a
tiny line segment that is perpendicular to that equipotential line at that
point. You will notice that in order for the extension of that line segment to
be perpendicular to other equipotential lines, it must nicely curve to meet this
property. Try to extend that tiny line segment both ways, always perpendicular
to equipotential lines, until they reach the point charges. Doing this, you
will be done with one field line. Draw a symmetric set of 10 field lines. The
final result should be similar to **Fig. 3.**

11)
Repeat the same procedure for the other charge distribution shown in **
Fig. 5b. **The final result should be similar to **Fig. 4.**

N/A

Comparison of The Results:

Compare the experimental field lines obtained with the corresponding figures in your text or lab manual.

Conclusion:** **To be explained by students

** **

Discussion:** **To be explained by students