PHY12L - E305 - ELECTRIC FIELDS AND EQUIPOTENTIAL LINES

ANALYSIS ON ELECTRIC FIELDS AND EQUIPOTENTIAL LINES

In experiment 305, which is entitled “Electric Fields and Equipotential Lines”, we studied the nature of electric fields by mapping the equipotential lines and then drawing in the electric lines of force using the conductive paper. The experiment was made easier with the help of the digital multimeter.

Electric field is defined as the electric force per unit charge. To determine the electric field E more precisely, consider a small positive test charge q at a given location.  As long as everything else stays the same, the Coulomb force exerted on the test charge q is proportional to q.  Then the force per unit charge, F/q, does not depend on the charge q, and therefore can be regarded meaningfully to be the electric field E at that point. We specify that the test charge q be small because in practice the test charge q can indirectly affect the field it is being used to measure. 

Coulomb’s law states that the electric force () is directly proportional to the magnitude of the charge (q) shown in the equation:

 

 

Or if shown by graph is,

The electric force () is also inversely proportional to the square of the distance of charges with each other (r) shown by the equation and the graph below.

 

 

 

 

 

 

 

 

 

 

 

 

 

Combining the two equations and removing the proportionality symbol, we will have the equation:

 

 

If, for example, we bring a test charge near the  Van de  Graaff generator  dome,  the Coulomb  forces from  the test charge redistribute charge on the conducting dome and thereby slightly change the E  field that the dome produces.   But secondary effects of this sort have  less and less  effect on the proportionality between F and q  as we make q  smaller. The direction of the field is taken to be the direction of the force it would exert on a positive test charge. The electric field is radially outward from a positive charge and radially in toward a negative point charge.  Electric field lines can be drawn using field lines. They are also called force lines.

The field lines are originated from the positive charge. The field lines end up at the negative charge.

(Positive charge electric field)

                                                                                    

 

 

 

	(Negative charge electric field)

 

                                                                                                                  

A positive charge exerts out and a negative charge exerts in equally to all directions; it is symmetric. Field lines are drawn to show the direction and strength of field. The closer the lines are, the stronger the force acts on an object. If the lines are further each other, the strength of force acting on a object is weaker.

Closely associated with the concept of electric field is the pictorial representation of the field in terms of lines of force.  These are imaginary geometric lines constructed so that the direction of the line, as given by the tangent to the line at each point, is always in the direction of the E field at that 2 point, or equivalently, is in the direction of the force that would act on a small positive test charge placed at that point.  The electric field and the concept of lines of electric force can be used to map out what forces act on a charge placed in a particular region of space.

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields. The interaction between a moving charge and the electromagnetic field is the source of the electromagnetic force, which is one of the four fundamental forces.

In some sources, definition of electric charge is a characteristic of some subatomic particles, and is quantized when expressed as a multiple of the so-called elementary charge e. Electrons by convention have a charge of −1, while protons have the opposite charge of +1.

In general, same-sign charged particles repel one another, while different-sign charged particles attract. This is expressed quantitatively in Coulomb's law, which states the magnitude of the repelling force is proportional to the product of the two charges, and weakens proportionately to the square of the distance.

The total electric charge of an isolated system remains constant regardless of changes within the system itself. This law is inherent to all processes known to physics and can be derived in a local form from gauge invariance of the wave function.

In physics, the space surrounding an electric charge has a property called an electric field. This electric field exerts a force on other charged objects. The concept of electric field was introduced by Michael Faraday.

The electric field is a vector with SI units of newtons per coulomb (N C-1) or, equivalently, volts per meter (V m-1). The direction of the field at a point is defined by the direction of the electric force exerted on a positive test charge placed at that point. The strength of the field is defined by the ratio of the electric force on a charge at a point to the magnitude of the charge placed at that point. Electric fields contain electrical energy with energy density proportional to the square of the field ntensity. The electric field is to charge as acceleration is to mass and force density is to volume.In the experiment, we are not required to solve for any values like the electric force or the intensity of electric field but rather we are asked to observe some properties of the electric field. We are able to do this by making a simple electric field that can be easily observed.  This can be done by using a conductive paper and a 6 volts battery to generate electric charges.  By using a silver ink pen, we are able to mark the electrodes on which the electric charges will pass.

 The objective of the experiments is to study the nature of electric fields by mapping the equipotential lines and then drawing in the electric lines of force. To start of the experiment, the materials used were conductive papers, silver ink pen, corkboard, push pins, connecting wires, circular template, digital multimeter and battery and as shown below:

 

 

 

	Conductive Paper
						Template, Push Pins and Wires
			Battery

 

 

 

 

 

The experiment consists of two parts. One is “Dipoles of Unlike Charges”. On the first part of the experiment, we searched for the points on the conductive paper that have equal potential. We have observed that when we connected the points with the same potential, the result is a parabola curve. We did five trials. The experiment is not very difficult since we have to find one point that has the same potential with the reference point. It requires patience.

Data obtained are the following:

Multimeter Reading (PART A)	Abscissa	Ordinate
.605 Volts	0	9
	-1	10.3
	-0.8	9.3
	-0.4	9.1
1.182 Volts	0	8
	-1.5	8.8
	-2.2	10
	-2.5	11
1.529 Volts	0	7
	-0.9	7.1
	-2.8	8
	-3.2	9
1.774 Volts	0	6
	-3.5	7.5
	-4.3	8
	-5.3	9
2.02 Volts	0	5
	-2.1	5.3
	-3.9	6
	-4.8	6.5

And as we graph the data, this figure was made. Showing that those blue lines were the data gathered, the equipotential lines form by the coordinates and by following the manual, that the electric field is perpendicular to the equipotential lines, those green lines were produced.

The distances of the equipotential lines are proportional to its distance to the point source. The closer the equipotential lines are to the source, the closer they are to each other.

          On the second part of the experiment, we followed the same procedure as the first. Here, instead of having on a point of negative charge, we made it surround the positive charge. The only difference is that we drew a circle that will serve as our guard ring and our point source is the origin. We have observed that after connecting the points with equal potential, the resulting figures were circles.

 

 

 

 

 

 

 

In this part, the following table was the results achived:

Multimeter Reading (PART B)	Abscissa	Ordinate
2.31 Volts	0	-1
	-1	-0.2
	-0.6	-0.9
	-0.8	-.07
3.47 Volts	0	-2
	-.08	-1.9
	-1.8	-0.9
	-1.5	-1
4.18 Volts	0	-3
	-1.6	-2.2
	-2.5	-1
	-2.8	-0.1
4.75 Volts	0	-4
	-1.2	-3.8
	-1.8	-3.4
	-2	-3.2
5.16 Volts	0	-5
	-0.9	-4.9
	-1.2	-4.8
	-1.5	-4.7

 

And the graph formed is below. Same formation and analyzation was made for blue lines were the data gathered, the equipotential lines form by the coordinates and by following the manual, that the electric field is perpendicular to the equipotential lines, those green lines were produced.

The small movement of the tester on the conductive paper will have a big movement on the reading of multimeter made the experiment slower and difficult.

Another thing is, tt is not possible for the equipotential lines to intersect each other, since they all follow the law of conservation of charge in which they must trade their charge to attain a new one.

          In the discussion of electric fields one can easily grasp its importance in our modern life from the compass used by early travelers to the technology used in our VCR’s. One example of which is electric motors which power our appliances and electric generators which produce electricity that run our world.

We can find electric fields in our everyday life and from there we can see the importance it has done for us.

The field generated in the experiment is produced from the special conductive paper, thus causing or making a hole in the paper would inevitably produce errors in the experiment. It is also a keen idea to take exact and precise measurements in order to make the graph as round as possible.

 

 

CONCLUSION ON ELECTRIC FIELDS AND EQUIPOTENTIAL LINES

Experiment 305, which is entitled “Electric Fields and Equipotential Lines”, aims to consider the nature of electric fields by mapping the equipotential lines and then drawing in the lines of electric lines of force.An electric field is an area where electrostatic force is present.On the other hand, equipotential lines are lines with equal potential.

          In the experiment, we used the conductive paper as the electric field. We plotted the points wherein the potentials are equal. The resulting figure was a parabola. We plotted the same coordinates on the negative x-axis. After doing five trials, we connected the five parabolas with a line intersecting perpendicularly. This is the electric line of force with direction from the positive to negative x-axis.

          We also plotted the points with equal potential on a guarded ring. Using the origin as our point source, we produced circles. This means that the electric lines are trapped inside the guard ring. The reason for this is that the guard ring can conduct electricity since it is made up silver. As we increase the distance from the point source, the voltage decreases.

In this experiment we can see that the equipotential lines generated are proportional in strength with respect to their distances from the point source, from this we can assume that the strength of the electric charge is proportional to its distance.