The objective is to (1) learn the concepts of electric field lines and equi-potential lines, and (2) use equi-potential lines to obtain field lines.
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
Electric field lines around a positive point charge are directed radially outward. The reason is what we have selected as the test charge. One unit of positive charge is defined as the "test charge." The best test charge the proton itself. Its charge is so small that it does not affect whatever field it is testing or measuring.
When test charges are placed around a positive charge (+q), they will be repelled and move radially outward. On the contrary, when test charges are placed around a negative charge (-q), they get attracted and move radially inward.
The field lines for a single positive and a single negative point charge are shown in Fig. 1.
Equi-potential surfaces around a single point charge are necessarily spheres centered at the point charge itself. At any point on an equi-potential surface (sphere), the potential is the same. That is the reason for the choice of word "equi-potential." In two dimensions (on paper), equi-potential surfaces become equi-potential lines (spheres become circles). It is important to note that any radial line (field line) is perpendicular to all equi-potential surfaces (circles) around a point charge.
It can be shown both mathematically and conceptually that regardless of the type of charge distribution, field lines are always perpendicular to equi-potential lines. This concept may be used find the trajectory of field lines around any type of charge distribution if equi-potential lines are known.
The field lines and equi-potential lines around an electric dipole are shown below:
The field lines and equi-potential lines around two parallel plates that are oppositely charged is shown below:
Equi-potential lines can be found experimentally by using a voltmeter. If we find points around a certain charge distribution that are at the same voltage, we may then connect those points to form an equi-potential line. After finding enough equi-potential lines, field lines can then be drawn perpendicular to them. This is one way to do it in a laboratory setting.
Two main types of charge distribution that will be used in this experiment are:
1) Two equal and opposite point charges (electric dipole), Fig. 5(a), and
2) two equal and opposite parallel surface charges, Fig. 5(b).
Figure 5 (a) Figure 5 (b)
Other charge distributions may also be examined due to capability of the available physics applet found at the following link: http://www.cco.caltech.edu/~phys1/java/phys1/EField/EField.html .
Use the Ag-200 silver solution and a thin brush to draw the above-mentioned two types of charge distributions on two separate sheets of conducting paper proportional to Figures 5a and 5b.
1) Place the conducting paper on the corkboard with a few sheets of regular size white paper underneath of it.
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 as in Fig. 5a, and with its other terminal search for points on the conducting paper that are equi-potential with Point A. At any of such points, the voltmeter should read zero. Locate a number of points that are 1 inch apart (at the most). Make a hole where each point is found by pressing a tack through the sheets and into the corkboard.
6) Due to symmetry, you will find that all points equi-potential with A fall along the dotted line as shown in Fig. 5a. In other words, the equi-potential line through Point A (selected on the perpendicular bisector of the line connecting the charges) is a straight line. However, the equi-potentials through Points B, C, D, and E will be curved lines.
7) Repeat steps 5 and 6 for each of Points B, C, D, and E. For any of these points you will find a curved equi-potential line.
8) Turn off the power, disconnect the voltmeter, and remove the tacks that were placed at the silver spots. Each student should obtain one sheet of white paper placed that were placed underneath the conducting paper that has got holes in it.
To each group member :
9) Circle the location of each charge and mark one as (+) and the other as (-). 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 straight or curved line that best fits each series of points. Such straight or curved line does not necessarily pass through every single point.
10) Once all equi-potential lines are drawn, the field lines can then be drawn keeping in mind that anywhere a field line crosses an equi-potential line the angle must be 90 o. Choose a point on one of the equi-potential lines and draw a tiny line segment that is perpendicular to that equi-potential line at that point. You will notice that in order to extend that line segment from either end of it and still have it perpendicular to other equi-potential lines, it must nicely be curved to meet this property or requirement. Try to extend that tiny line segment both ways while keeping it perpendicular to other equi-potential lines until it reaches each of the point charges. Doing this, you will be done with the drawing of 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. Of course, the metal tacks for wire connection may be pushed in at the end spots shown in Fig. 5b. Your final drawing should be similar to Fig. 4.
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.