Electric Fields Theory: An electric field is a region in space in which electric forces act on electric charges, if present. The electric field strength for any point in space is defined as the net electric (Coulomb) force per unit of positive charge acting on a charge placed at that point, i.e.,   [1] E=F q The SI unit for electric field is Newton / coulomb N/C, or (more practically) volt/meter, V/m. The direction of an electric field at any point is defined as the direction of the net electric force on a positive charge placed at that point. Faraday introduced the concept of lines of force to aid in visualizing the magnitude and direction of the total electric field about a charge or collection of charges. These concepts are listed below. 1. A line of force is everywhere tangent to the electric field direction. 2. The lines of force originate on positive charges and terminate on negative charges. 3 The density of the lines of force (i.e. the lines/cm or lines/cm2) in a region of space is used to represent the electric field strength in that region of space. 4 Lines of force will not cross over or touch one another. Electric fields can be represented by a scaled drawing, by first choosing a scale factor (proportionality factor) so that n number of lines/cm2 represent a certain value of field strength (volts/m).

(a)

(b) Figure 1

Examine the figure above. The two figures represent an electric field departing a charged sphere. If we let figure 1(a) represent an electric field with field strength of E, figure 1(b) would represent an electric field with field strength of 2E. (Twice the numbers of field lines departs the charged).

In this experiment, we may estimate the electric field at certain points from the potential gradient, at these points E = ∆V/∆x = (V 2 – V 1 ) / (x 2 – x 1 )

[2]

Where V 1 and V 2 are the potential of two adjacent equipotential lines and (x 2 – x 1 ) is the distance between the lines in meters. It is possible to find any number of points in an electric field, all of which are at the same potential (voltage). If a line or surface is constructed such that it includes all such points, the line or surface is known as an equipotential line or surface

Procedure: A. Electric field produced by a charged rectangle-triangle configuration. Setting up the experiment 1. □ From the tray, remove the conductive sheet that has the rectangle-triangle configuration also remove the two long wires with a clip on one end. Notice that the conductive sheet has pins extended from the surface of the copper foil for each shape. These pins will be utilized to make an electrical connection to the power supply. □ Turn on the power supply and using the multimeter measure across the DC output, adjust the voltage for 15V DC. □ Use the red wire, connect the triangle to the positive (+) side of the power supply and the black wire to connect the rectangle to the negative (-) side of the power supply. □ To ensure that the voltage connection is distributed along the copper surface, measure the potential between the triangle and rectangle, by touching the probes to the copper surface it should be the same as that measured across the power supply. □ For the remainder of the experiment you will make voltage measurements in respect to the negative of the power supply. For the best connection, replace the black probe of the multimeter with the short black wire included in the tray. The wire connectors are stackable, plug one end of this wire into the wire connected to the negative of the power supply, and plug the other end into the COM socket of the multimeter. NOTE: Do not mark on the conductive sheet use the grid sheets that are provided with this unit. Do not press down on the probe so hard that it leaves indentations into the conductive paper. Finding the first equipotential line 6 □ Start at the point indicated on the illustration to the right and measure the potential at this point. □ Mark on the grid sheet the approximate position.

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To obtain an equipotential line you are required to find Start Here 5 to 7 points on each side of the centerline a point that is of approximately equal value (i.e.± 0.05 v) to the first measured point. □ Start at the next grid mark above or below the initial point and parallel to the rectangle; find a potential approximately equal to the first measured point. □ Mark the approximate position of this point on the your grid sheet not the conductive sheet. □ Continue in this manner until the required numbers of points are located above and below the center line. These points should span beyond the length of the rectangle such that you show that it is beginning to wrap around the rectangle front edges.

□ Draw a smooth line to connect the points. Label it with the measured voltage potential. This is your first equipotential line. Finding the remaining equipotential lines 7. □ Repeat steps 6 for points 2cm, 3cm, 4cm and 4.5 cm along the centerline away from the rectangle and towards the triangle. The 4.5 cm point will be nearest to the triangle. Remember to record the voltage for each equipotential line. Drawing in the field Lines 8. After all the equipotential lines are drawn you are to draw in the electric field lines. Electric field lines are perpendicular to the equipotential lines. □ Read this step entirely before drawing the lines. The field line starts perpendicular from one + surface or line and is drawn to the next surface or line to end perpendicular into that line. Keep in mind when drawing 2 86V 12 66V these lines that electrons will not 44 make sharp angled turns, but 11 23V 66 8 94V would turn in a curvature. Continue drawing in the field line going from one equipotential line to the other finally terminating into the triangle. □ Start from the rectangle and draw 7 field lines 1 for each grid mark along the rectangle’s front surface and 1 each centered on the top and bottom narrow side of the rectangle. Assigning Regions 9. □ Electric field strength would be Strongest where they emerge from or terminate onto a sharp point. Intermediate electric field strength would lie in an area where electric field lines are running parallel to each other with equal spacing between them. A Weak electric field would be in an area where the electric field lines and the equipotential lines are farther apart or in a region where there is no electric field. You should realize that the lines that you have drawn are only a small sampling of those that are actually present. Just keep in mind that electric field lines do not cross over one another. □ Using the explanation above, and other than the inside the triangle, indicate on the diagram a region where you think the electric field is (S) Strongest, (W) weakest, and (I) intermediate.

Determine the Electric Field Strength 10. □ The areas that you have indicated on your diagram, (S), (I) and (W), should be between two equipotential lines. Note that the triangle and rectangle are also equipotential lines (surfaces). Record the values of the two nearest equipotential lines for each region indicated on your diagram. □ At each indicated region measure the distance between the equipotential lines, and record into data table 1. □ Calculate the electric field strength for each region using equation [2].

Data Sheet Table 1 Triangle and Rectangle combination.

region

Voltage of nearest two equipotential lines (V)

∆V

distance between lines (∆x)

Electric field strength (E) V/m

Strongest Intermediate Weakest

Measured voltages at different points within the triangle. 1.) From the measured voltages within the triangle and using equation [4]. What can be deduced about the electric field within the triangle?

2) Electric field line start on __________ charges and terminate on _________ charges.

3) Electric field lines are ________________ to equipotential lines.

4.) Below is a figure depicting a uniform electric field. Next to it draw a uniform electric field 3 times its strength.

Grid Sheet