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Objectives:__

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

2) use the equipotential lines for drawing the electric field lines.

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Equipment:__

A computer with the Internet connection, paper, and pencil

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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 surface charges (similar to a parallel-plate capacitor).

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Procedure:__

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 equipotential 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 step.** A
collection of these statements will constitute your conclusion
of the experiment. Also, after each step that is marked by (**),
draw the equipotential lines **only **as you see them on the applet.
Then draw the field lines yourself. In order to draw the filed lines by
yourself and from your intuition and artwork, you
may have to repeat that part and have the field lines in the "deselect" mode as
well. After the first step, you may have to read
this paragraph again so that you do not miss anything.

Click on the following link**:**
http://www.cco.caltech.edu/~phys1/java/phys1/EField/EField.html . The
"Electric Field Applet" appears. For simplicity only have the "electric
field lines" and the " Equipotential 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, let's 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 "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
(where proportionally the left point is)**.** A
red spot or (+) sign will appear that shows the existence of
+1 unit of charge. You can immediately see
the equipotential 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 equipotential line."

A1**.**1) Now, **if you reset** the applet and do the
same with a **(-1) **unit of charge, you will
immediately see the equipotential 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 equipotential 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 proportionally 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 equipotential
lines as **nonconcentric
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
equipotential 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
equipotential 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 equipotential 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 equipotential line."

**B) Field Lines Orientations
of Equal Charges**

B1) Try a **(+3)** at
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 field lines. Also note that the
equipotential 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 equipotential line."

**C) Field Lines Orientations
of Non-equal Charges **("In each case, pay attention to the way
each field line crosses each equipotential line.")

C**1**.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?

C**2**.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
equipotential 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.

D**1.**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**.

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

D**2.**1) Create two vertical lines (planes) of
same but equal charges and observe the result.

D**2.**2) Create two vertical lines (planes) of
same but different charges and observe the result.

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**:**

** **

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