EXPERIMENT 10

ELECTRIC FIELDS AND LINES OF FORCE

INTRODUCTION:

        A fixed distribution of electric charge causes an electric force to act on every other electric charge in the universe.  Another very convenient way to look at it is to say that the charge distribution sets up an electric field E at every point in space, and that it is the field that causes and electric force on the other electric charges.  This experiment will serve to examine certain electric fields; and in particular to map the equipotential lines of an electric field and hence determine the electric lines of force.

THEORY:

        The first quantitative investigation of the law of force between electrically charged bodies was carried out by C. A . Coulomb in 1784-1785.  His measurements showed that the force of attraction for unlike charges or repulsion for like charges followed an inverse square law of distance of separation.  It was later shown that for a given distance of separation r the force is proportional to the product of the individual charges Q and Q’, and is a function of the nature of the medium surrounding the charges.  Expressed in symbols, Coulomb’s law is

                                                                                        (1)

 where the factor K, called the dielectric constant, is introduced to take care of the nature of the medium.  The factor K is arbitrarily assigned a value of 1 for empty space.  Coulomb’s Law is restricted to point charges, that is, the charged body must have dimensions which are small compared to the separation distance.

       Several systems of units, each with its particular advantages, are in use.  The electrostatic system will be emphasized in this experiment.  In the electrostatic system forces are expressed in dynes, distances in centimeters, and the unit of charge, called the statcoulomb, is chosen of such magnitude that the proportionality constant in coulomb’s law is equal to unity.  Thus coulomb’s law may be expressed by,

                                                                                                                                    (2)

       When all quantities in equation (2) are unity the definition of the electrostatic unit (esu) of charge or statcoulomb is indicated.  The factor K in coulomb’s law, called the dielectric constant of the medium, is assigned a value of 1 for vacuum.

       An electric field, commonly called field of force, is a region in which forces act on electric charges if present.  If a force F acts on a charge q at a point in the field, the field strength E, by definition the force per unit charge, is

                                                                                                                                 (3)

that is the magnitude of electric field strength is the force per unit charge.  Force is a vector quantity having direction as well as magnitude.  The direction of an electric field at any point is the direction of the force on a positive test charge placed at the point in the field.

       Lines of force are used to visualize the strength and direction of an electric field.  A line of force is the path which a free test charge would follow is traversing the electric field.  The path is everywhere tangent to the field direction at each point.  As an illustration, consider the isolated positive charge Q placed at A in Figure 1.  A small positive test charge q at any point in the field experiences a radial force of repulsion from A.  The lines of force are drawn with arrows to point this direction.  When Q is a negative charge, that is an excess of electrons, these lines would be directed towards A to indicate an attraction of the positive test charge q.

       The diagram of Figure 2 shows a plane section near a pair of equal charges of opposite sign.  Each charge exerts a force on a unit test charge placed in the field.  The resultant force is the vector sum of these forces.  Thus, at a point b, f₁ is the repulsion force on the unit test charge due to the positive charge on A, and f₂ is the force of attraction to the negative charge on B.  The resultant R is tangent to the line of force at the point b.

Figure 2: Electric Field Near Two Equal Charges of Opposite Sign.

       It is evident that a uniform field is represented by a set of parallel lines of force.  A converging set of lines of force indicates a field of increasing strength; while a field of decreasing strength would be represented by a diverging set of these lines.

       It is possible to find a large number of points in an electric field, all of which have the same potential (voltage drop from a given reference).  If a line or a surface is so drawn that it includes all such points,  the line or surface is known as an equipotential line or surface.  A test charge may be moved along an equipotential line or over an equipotential surface without doing any work.

       The electric field or lines of force are everywhere perpendicular to the equipotential surface.

THE EXPERIMENT:

 1.  Apparatus

             Your lab station should be equipped with the following:  Field mapping board and U-shaped probe, Figure 5.  Eight similar resistors connected in series (A to I in Figure 5) and mounted on this board.  Field plates with conductive and corresponding template.  Source of potential.  Sensitive galvanometer as a null-point detector.

Figure 5:  Diagrammatic Representation of Electric Field Apparatus.

2. PROCEDURE:

            In order to begin using the power supply, you should set its current limit lower than the maximum safe current for the device to be powered.

            For this experiment you will use a current of 0.2 A and a voltage of 4 V.  You will have to follow these procedures in order to get these set.

1.      Push both tracking buttons (No. 15 of Figure 6) outs, so that you in the independent mode.

2.      With the test lead (cable) temporarily short the positive and the negative output terminals of the left output terminals (no. 13 of Figure 6).

3.      Rotate the VOLTAGE knob (knob 14 of Figure 6) away from zero sufficiently to light the C.C. indicator.

4.      Set the  meter selection switch to AMPS (switch 2 of Figure 6) so that the LED display show the current (no. 1 of Figure 6).

5.      Adjust the CURRENT knob (knob 10 of Figure 6) for the desired current limit.

6.      The value appearing in the LED display should be around 0.2 A, this is your preset current.

7.      Remove the short between the positive and negative output terminal.  Notice:  The LED will display 0.00 A after you remove the cable, that is because you have an open circuit you shouldn’t worry about this.

8.      Turn the  meter selection switch to VOLTS so that the LED display show the voltage.

9.      Adjust the VOLTAGE knob for the desired 4 V value.

10.  The value appearing in the LED display should be around 4 V, this is your preset voltage.

       Now you should prepare the electric field mapping apparatus.  Turn the field mapping board over and notice the two metal bars.  Each bar has two threaded holes.  Two of these holes hold plastic-headed thumb screws with knurled lock nuts.  Remove these thumb screws.  Now center any one of the field plates in such  a manner that the holes in the plate coincide with holes in the metal bars.  Insert a thumb screw into each hole and turn it until it touches the board below.  Turn the knurled lock nut to hold the field plate securely in place.  Turn the field mapping board right-side-up.

            Binding posts marked “Bat.” and Osc.” are located on the upper side of the board.  Connect the DC power supply to the appropriate binding post (point X and Y in Figure 5).  When the voltage  is applied to the terminals, charges flow between them across the field plate following the lines of force of the electric field established.  This same potential difference will be equally divided between the end terminals of the series of similar resistors.

       Fasten a sheet of graph paper to the upper side of the board.  The paper is secured by depressing the board on either side and slipping the paper under the four rubber bumpers.  Select the design template (plastic template) containing the field plate configuration you have chosen.  Place the design template on the two metal projections (template guides) above the paper edge and let the two holes on top of the template slide over the projections.  Trace the design corresponding to the field plate pattern in place on the underside of the mapping board and remove the template.

       Carefully slide the U-shaped probe onto the mapping board with the ball end facing the underside of the field mapping board.  Connect one lead of the null-point detector (galvanometer) to the U-shaped probe and one to one of the banana jacks, which are numbered E1 through E7.

       Notice the knurled knob on the top of the probe (adjacent to the spotting hold) and the screw below the probe with one finger of one hand resting lightly on the knurled knob, and a finger of the other hand lightly contacting the nut of the leg.  The leg slides on the table top and in so doing stabilizes the probe.  Do not apply pressure to the probe, and avoid squeezing its jaws.

            Using the selected banana jack, move the U-shaped probe over the paper to a zero reading of the galvanometer (Make sure that the galvanometer does not go off scale, that will damage it).  The circular hole in the top arm of the probe is directly above the contact point which touches the graphite-coated paper.  Record the location of the equipotential point directly on the paper.  Move the probe to another null-point position and record it.  Continue this procedure until you have generated a series of these points across the paper.  All the points corresponding to the same equipotential curve should be labeled with the number of the corresponding resistor (i.e. E1 or E2...etc.).  Connect the equipotential points with a smooth curve to show the equipotential line of that banana jack.  For example the series of points C’, all of the same potential as C in Figure 5, define an equipotential line.

            Connect the detector to a new banana jack and plot its equipotential line.  Repeat until equipotential lines are plotted for all banana jacks E1 through E7.  Since the potential difference is the same across each similar resistor, the equipotential lines obtained will be spaced to show an equal potential drop between successive lines.

            With the help of a voltmeter record the potential drop across each series resistors and record in Table 1 of your lab report.

            Upon completion, select a different field plate and repeat the above procedure until all electric fields from all the provided plates are drawn.

3.  ANALYSIS:

             The flow lines or lines of force are everywhere perpendicular to the equipotential lines.  Draw in, by dash lines, the lines of force for the electric fields studied.