### Experiment 1

#### Electric Field Mapping

Objectives:

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.

Equipment:

A computer with the Internet connection,  paper, and pencil

Theory:

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.

Figure 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.

Figure 2

The field lines and equi-potential lines around an electric dipole are shown below:

Figure 3

The field lines and equi-potential lines around two parallel plates that are oppositely charged is shown below:

Figure 4

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 will also be examined due to capability of the applet at hand.

Procedure:

You may need to add the following Website to your Java exception list:  http://www.cco.caltech.edu/

To do this, follow the path (Windows operating system),

Start → All Programs → Java → Configure Java → Security (use High) → Edit Site List … → Add → Type in the site URL  http://www.cco.caltech.edu/.

This experiment, exceptionally, does not require a formal lab report.  You will instead follow the experimental procedure and will be asked to draw the electric field lines for a few selected cases.  Your drawing of the electric field lines will of course be based on the equi-potential lines you will observe on the applet.  You will have fun doing this experiment.  Make sure that you write a statement or more after each drawing.  A collection of these statements will constitute your conclusion of the experiment.

For each case that is marked by (**), draw the equi-potential lines only as you see them on the applet.  Then draw the field lines yourself applying the perpendicularity concept.  In order to draw the filed lines by yourself using your intuition and artwork, you may have to repeat the applet for that part and and this time have the field lines in the "deselect" mode.  After the first step, you may have to read this paragraph again so that you do not miss anything.

The "Electric Field Applet" appears.  For simplicity only have the "electric field lines" and the " Equi-potential lines" selected.  Deselect all other options.  You may place several units of (+) or (-) charges at any point on the  dark area of the applet.   In the small horizontal window of the applet (on the top right side),  you may move the tiny vertical bar to the right or left to change the size and the sign of the charge (s) you want to place on the applet's screen.  Let's name this tiny window the " charge selection window."  Follow the systemic approach below:

A) Forming the Field lines Orientation of an Electric Dipole:

A1) First, form an electric dipole proportional to what you see in Fig. 5 (a).  Place a (+1) unit of electric charge on the left side and a (-1) unit of charge on the right side where Fig. 5 (a) indicates as "point charges."   To select a (+1) unit of charge, click on the right or left side of the charge selection window until it shows (1) unit.   Then click on the dark area once.   A red spot indicating  (+) sign will appear that shows the existence of +1 unit of charge.

You can immediately see the equi-potential lines as concentric red circles around the single (+1) unit of charge with white electric field lines drawn radially outward.  The applet does not place arrowheads on the white field lines "Pay attention to the way each field line crosses each equi-potential line."

A1.1) Now, if you reset the applet and do the same with a (-1) unit of charge, you will immediately see the equi-potential lines as concentric blue circles around the single (-1) unit of charge with white electric field lines drawn radially inward.  The applet does not place arrowheads on the white field lines Go ahead and try this to see the field lines as well as the equi-potential lines of each type of charge when each single charge is just alone by itself.  Afterwards, reset the applet; repeat part (A1) again, skip part  (A1.1) and proceed to Part (A2).

A2)  With a (+1) unit already placed on the left, select a (-1) unit of charge.  Do this by adjusting the charge selection window to (-1) unit  Then click on the dark area once (where nearly the right spot in Fig. 5 (a) shows).   A blue spot will appear that shows the existence of -1 unit of charge.  You can immediately see the equi-potential lines as non-concentric blue circles around the charge with white electric field lines not drawn radially inward.  The applet does not place arrowheads on these field lines either.  There are no single charges any more!  The field of each charge affects the field of the other.  The equi-potential lines are not concentric circles anymore.  What you see is the field lines orientation of an electric dipole.  Pay attention to the way each field line crosses each equi-potential line.

A3) Reset the applet and repeat the same experiment with (+2) units and (-2) units of electric charges.  You should see more (denser) field lines in each step.  Pay attention to the way each field line crosses each equi-potential line.

A4)** Reset again, and experiment with (+4) and (-4) units of charges and see how the density of field lines changes.   Pay attention to the way each field line crosses each equi-potential line.

B)  Field Lines Orientations of Equal Charges

B1)  Place a +3 on the left spot with another +3 at the right spot.  You know that like charges repel each other.  You will see this effect in the way field lines curve.  Also note that the equi-potential lines become closer to being circles as we move further away from both charges.  You can see the best symmetric results if you place the first (+3) at a point where it causes one of the field lines to be exactly horizontal.  This can be achieved by a few trial and errors.  Of course, you need to reset before each trial.  Once you get one horizontal field line, then place the 2nd  charge somewhere on that line.  It will result in a nice and symmetric field lines orientation.  The supposedly outward arrows on the white field lines are not shown on the applet.  Pay attention to the way each field line crosses each equipotential line.

B2)**  Repeat B1 but with two (-3) charges.

The supposedly inward arrows on the white field lines are not shown on the applet.  Pay attention to the way each field line crosses each equi-potential line.

C)  Field Lines Orientations of Non-equal Charges

In each case, pay attention to the way each field line crosses each equi-potential line.

C1.1)  Reset the applet.  Place +2 on the left and -1 on the right and observe the effect.

C1.2)**  Reset the applet.  Place +5 on the left and -2 on the right and observe the effect.

C1.3)  Reset the applet.  Place +6 on the left and -1 on the right and observe the effect.  How many field lines of the (+) charge are occupied with the lines of the (-) charge?

C1.4)  Reset the applet.  Place +9 on the left and -1 on the right and observe the effect  How many field lines of the (+) charge are occupied with the lines of the (-) charge?

C2.1)  Reset the applet.  Place +2 on the left and +1 on the right and observe the effect.

C2.2)**  Reset the applet.  Place +6 on the left and +2 on the right and observe the effect.

C2.3)  Reset the applet.  Place +9 on the left and +1 on the right and observe the effect.

C2.4)  Reset the applet.  Place +9 on the left and +1 on the right closer to the (+9) and observe the effect.

C2.5)  Reset the applet.  Place +9 on the left and +1 on the right farther to the +9 and observe the effect.

D)  Field Lines Orientations in Between Two Parallel Plates Equally But Oppositely Charged

In each case, pay attention to the way each field line crosses each equi-potential line.

To arrange two vertical lines of charges as shown in Fig. 5 (b), you need to first make one vertical line by a number of (+) charges and another vertical line with a number of (-) charges.  Use (+2)s and (-2)s for this purpose.  You may have to try and reset a few times to get it right.

D1.1)  Make a (+) vertical line by placing 8 (+2) units of charge 0.5 inches apart vertically.   Then make a (-) vertical line by placing 8 (-2) units of charge 0.5 inches apart vertically.  The positive and negative lines must turn out parallel and about 1 to 1.5 inches apart.  When all 16 points are placed fairly accurately, you will see a nice symmetry.  You will also see that the field lines (the white ones) in between the parallel plates of opposite charges are essentially parallel.

D1.2)**  First reset the applet and then repeat D1.1 with (+3) and (-3) charges.

D2.1)  Create two vertical lines (planes) of same sign and equal (amounts) charges and observe the result.  Example: Lines of (+2)s and (+2)s.

D2.2)  Create two vertical lines (planes) of same sign but different (amounts) charges and observe the result  Example: Lines of (-2)s and (-3)s.

Data:  N/A

Calculations:  N/A

Comparison of The Results:

Compare the field lines obtained with the corresponding figures in this lab manual.

Conclusion:

Your conclusion must include:

### 2) your drawing of the field lines based on the equi-potential lines you drew from the applet where requested by the (**).

Discussion:  To be explained (if necessary) by students.