EQUIPOTENTIAL CURVES AND LINES OF FORCE


PURPOSE:	In this experiment you will study the properties of electric fields by mapping 
equipotential lines and constructing the corresponding lines of electric force.

THEORY:	Although it is relatively easy to calculate the electric field strength and the 
potential in the vicinity of a few point charges or certain rather simple charge distributions of 
high symmetry, in the general case the calculations may involve repeated numerical integrations 
of partial differential equations which are feasible only with high-speed computers.

Usually it is simpler and more direct to map the field experimentally.  This may 
be done by locating a number of points having the same electric potential; when 
these points are connected together, an equipotential surface is traced out.  By 
repeating this process for other values of the potential, a representation of the 
entire electric field is obtained.  The set of equipotential curves may be thought 
of as being analogous to the contour lines of equal elevation on a topographical 
map.

From the set of equipotential curves, another set, the lines of force, may be 
obtained; the lines of force are everywhere orthogonal (perpendicular) to the 
equipotential curves.  Stated in more physical terms, the electric lines of force 
are everywhere in the direction for which the change in potential per unit 
distance is a maximum.

PROCEDURE:	The apparatus consists of a shallow rectangular pyrex baking dish with 
Cartesian paper taped to the outside bottom.  Weakly conducting tap water is placed in the dish 
and a set of stationary electrodes is placed in the water.  The electrode configuration consists of 
two point electrodes.  Thus, the experiment will map the two dimensional representation of the 
equipotential surfaces of an electric point dipole.

Set the point electrodes symmetrically spaced over the coordinate paper along 
the long center line (y-axis) with a spacing of approximately 20 cm (one at -10 
cm, the other at +10 cm).  Record the (x,y) coordinates of the point electrodes 
so that they can be replaced if they are accidentally moved.  Mark the positions 
of the point electrodes on a piece of Cartesian graph paper.

Adjust the DC power supply to give an output of 12 volts.  Use the digital 
multimeter to make this adjustment.  Connect the negative terminal of the 
multimeter to the negative output of the power supply (positive terminal of the 
multimeter to the positive output of power supply) (Figure 1).

Leaving the negative terminal of the multimeter connected to the negative 
output of the power supply, place the positive terminal of the voltmeter in the 
water and locate the locus of points which are at a potential of 2.0 V with 
respect to the negative point electrode.

A way to do this is to sweep the movable probe of the voltmeter along both 
major coordinate axes of the graph paper attached to the pyrex dish and locate 
all points for which the voltmeter reads 2.0 volts.  Remember to keep the 
movable probe vertical, and be careful of parallax as you observe the position of 
the probe over the coordinate paper.  Do not bother to record the coordinate of 
each point; simply plot the point on your graph paper as you determine it.  
When finished, draw a smooth dashed curve through the points and label it as 
the 2V equipotential surface.  Does the dashed curve exhibit the expected 
symmetry?  Repeat the procedure for 4V, 6V, 8V, and 10V surfaces, 
remembering to label each of the resulting dashed curves.

	ECLF-1
Construct the electric field lines by drawing solid lines from one point electrode 
to the other, being careful to cross each of the dotted equipotential curves at 
right angles.  Draw at least 5 electric field lines, one being the shortest line 
between the point electrodes, then 2 each on both sides of this first line.  Place 
arrows in the field lines representing the direction of the electric field.

Figure 2 is representative of the equipotential curves and field lines expected for 
an electric point dipole.  How does your result compare?

Electric field lines have a directional arrow associated with them.  Why do the 
equipotential curves have no direction associated with them?  In what region of 
space does your data suggest the magnitude of the electric field is greatest?  
Why?



		 








						Figure 2
							Representations of electric field
							(solid lines) and equipotential curves
							(dashed lines) for an electric dipole.

















	ECLF-2