GUIDE QUESTIONS 1. Is it possible for equipotential lines to intersect each other? Justify your answer.
Yes, it is possible for equipotential lines to intersect each other if and only if the two charges have the same charge (positive-positive or negative-negative), same value of the potential as each other, and they are emerging from or converging to the same singularity.
2. From the electric field pattern you obtained, what is the relationship between the spacing of the field lines and the electric field magnitude? It is not quite seen in the pattern drawn but more likely, the closer the field lines are to each other, the stronger the electric field magnitude will be. By the equation and graph it is said that the electric force is also inversely proportional to the square of the distance of charges with each other. 3. If an electron is at the midpoint of the line connecting two equal but opposing charges in a direction perpendicular to this line, does the charge experience zero electric force due to the two charges? If not is there a point along the line connecting the charges where the electron will experience a zero electric force? Where is this point located?
The charge does not experience zero electric force because for the point midway between the forces acting on the electron are in same line but also in the same direction so they will add. The force will be zero only at infinity because between the charge forces will add but beyond forces will oppose but they would never be equal in magnitude.
4. Sketch the electric fields between two positive charges of equal magnitude.
ANALYSIS Voltage is the electric potential difference between two points, or the difference in electric potential energy of a unit test charge transported between two points. There is no potential difference since the points are on a line of equipotential. Electric field is the measure of particle’s ability to attract or repel other charged particles. Electric force of attraction or repulsion between two particles is the consequence of electric field of each particle. Meaning, whether a particle is near other particles or not, its electric field is still present. 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. 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 surround the particles by using a guard ring. It was observed that the equipotential lines that are formed are circles. Therefore, equipotential lines would tend to have a circular shape when the opposite charge encloses the point source. The data gathered in part A shows that the farther the coordinate is from the fixed point the higher is its voltage. This is both true to the different points given, in the positive and the negative coordinates. However, the data in part B shows that distance is inversely proportional to the voltage. The electric field inside the guard ring will travel in the same direction of the magnetic field of the guard ring since it is in a circular shape. Consequently, the electrical field inside the guard ring is traveling inside and it does not outrun it, it is like you put several other rings onto the guard ring. The several rings signify the electric field.
CONCLUSION Our group was able to study the nature of electric fields by mapping the equipotential lines and then drawing in the electric lines of force or electric field lines which are always perpendicular to each other. An electric field is an area where electric force is present while equipotential lines are lines with equal potential.
For experiment 1, plotting the points with equal potentials produce a parabolic figure and then the field lines are drawn intersecting the po tential lines perpendicularly. For experiment 2, we produce circular potential lines and so the electric field lines are all radii of the guard circle and the other circles since we produce concentric potential lines.
Performing this experiment, it is concluded that equipotential lines are proportional in strength with respect to the distances from the point source. Finally, voltage is indirectly proportional to the distance from the point source.
ABSTRACT Experiment no. 305 is about Electric fields and equipotential lines. The purpose of this experiment is to experimentally investigate the relation between electric field lines of force and equipotential surfaces in two dimensions. We will construct various conducting surfaces (metal electrodes) and study the electric field and equipotential patterns associated with them.
INTRODUCTION Electric field E is a vector quantity; it is defined as the force per unit charge that would act upon a unit positive test charge if the charge were placed at the point in question. A line of force or electric field line is the path a charge would follow if it were allowed to move along in exactly the direction of the force acting on it. By convention, the sense of E is the direction of the force on a positive test charge. The potential difference, (between two points A and B) is defined as the work that would have to be done in moving a unit charge from point A to point B. The sign of V may be positive or negative. Work can be expressed as force times distance, where the force acting on the charge is due to the electric field at the location of the charge, F = qE, and the distance is measured along the direction of the force. The calculus and non-calculus form of the equations which relate V and E are given below. The electric field at a point is:
where r is a unit vector in the direction of greatest change in V. If Eq. (1) is integrated over l (or both sides are multiplied by ∆l), the potential difference between points A and B is found:
where dl or ∆l are infinitesimal or finite, but small, line elements, respectively, along a given path. Since the work done in moving a test charge from A to B (and consequently the potential
difference between A and B) is independent of the path for a conservative force, you can choose a path which makes the integral or sum of Eq. 2 easy to evaluate. If you have studied calculus, it is preferable to use the line integral.
For a constant E, as in the case of the parallel plate capacitor, V = E l cos θ. Potentials are often defined relative to some standard reference point that is taken to be zero. The reference point is often referred to as ground. The MKS unit of potential is joule/coulomb that has been given the name volt. If a test charge is moved in a direction perpendicular to E, no work is done (see Eq. 2). Therefore, there is no change in electric potential. Such a path is an equipotential surface. Since there is a potential and electric field value at every point in space, there is no limit to the number of field lines and equipotential surfaces. In this experiment you will work in two dimensions to acquire a family of lines spaced at convenient intervals.
METHODOLOGY The materials used were conductive papers, silver ink pen, corkboard, push pins, connecting wires, circular template, digital multimeter and battery. The experiment consists of two parts. One is “Dipoles of Unlike Charges” and the other is “Point Source and Guard Ring”. On the first part, we take the cross hair of the paper as the origin marking (0,10) and (0,-10) coordinates of the conductive paper using the silver link pen on a hard surface. Then we placed push pins on the marked coordinates that serves as the electrodes. We connect the electrodes to the battery using the alligator type connecting wires. Equipotential are plotted by touching one probe of the multimeter to one of the electrode push pins. This will serve as the reference. The other probe of the multimeter is used to measure the potential at any point on the paper.
In mapping the equipotential line, we set at least 1 cm distance from the reference electrode and start moving the probe to a desired potential indicated on the multimeter. Take note of the x and y coordinates.
On the second part, we repeat the experiment using a different electrode configuration: a point source and a guard ring. The point source is located at the origin of the conductive paper. We set the radius of the ring to 7 cm. placing the push pins at the center and at (0,-7cm).
