PHYS 2426 – Engineering Physics II

Electric Field Mapping II – Additional Geometries

 

Leader: _____________________________  Recorder: ___________________________

Skeptic: _____________________________ Encourager: _________________________

 

Materials

Electric Field Mapping Apparatus with rectangular, triangular and circular plates

3 x Point Probes                                              

DMM                                                             

2 Sheets Quadrille Graph paper (one laminated)

4 x Banana plug cables                                    

Battery Eliminator

15” Ruler

 

Introduction

      In this activity we will use the same apparatus and procedure as in the previous lab to map the electric field for some additional geometries of conducting plates.  In particular instead of two parallel plates, we will look at the field pattern created when a potential difference is placed between a rectangular plate and a circular plate, and a rectangular plate and a triangular plate.  The first geometry we will explore is shown in Q1. 

 

Q1)  You will connect the + terminal of the power supply to a round plate and the – terminal to the rectangular plate.  On the figure sketch what you think the electric field lines will look like for this geometry and then sketch what you think the equipotential surfaces will look like.  Use a solid line for the field lines and a dotted line for the equipotential surfaces.

Q2)  Explain your reasoning for your answer to Q1).

 

 

 

 

 

Procedure

1. Set-up the Apparatus

      To set up the experiment, first determine the scale of the graph paper by measuring the spacing in cm for 10 grids and divide by 10.  Record the spacing between the grids on the graph paper in the space below.  

 

Q3)  Spacing per grid = ________ cm/grid

 

      Next, place the graph paper underneath the dish so that the grid lines run parallel to the edges of the dish.  Place the stainless strip with its long edge parallel to the short edge of the dish, and so that its inner edge is centered on the axis of the graph paper.  Place the circular disk so that it is centered on the same axis and its closest edge is 20 grid lines from the edge of the strip. Place the tip of two of the probes on each of the conductors.  Fill the dish with water until the conductors are just covered by the water. 

      Using the provided banana plug cables, connect the + terminal of the power supply to one the probe touching the circular plate and the - terminal to the other probe. We will refer to the conducting plate connected to the + terminal of the power supply as the + conductor and the conducting plate connected to the – terminal of the power supply as the – conductor.  It is customary to use a red wire for the connection to the positive side, and a black wire for the connection to the negative side. Set the power supply to 6 V and turn it on.    

 

2.  Setup the DMM

      Connect the COM lead from the digital multimeter (DMM) to the remaining point probe.  The connectors on the back of the probe will unscrew revealing a hole in the connector that you can put the probe into.  Tighten down the connector to hold the probe and make a good contact.  Turn the dial on the DMM to the 20 V DC setting.  The DC side is indicated by a solid line over several dashed lines.  Place the probe connected to the VΩ lead on the DMM on the conductor connected to the plus side of the power supply and the other probe connected to the DMM on the other conductor.  The meter should give a reading approximately equal to the setting on the power supply, if it does not, contact your instructor.

 

3. Preliminary Measurements

      We will alter the procedure slightly from the previous lab activity.  Place the point probe connected to the COM lead on the DMM on the - conductor.  Move the lead connected to the VΩ terminal on the DMM toward the circular from the rectangular plate along the axis of the graph paper until you find a point that reads a potential difference of 1.2 V.  Record the location of the point in figure 1.  Next find the location along the axis at which the potential difference is 2.4 V to the rectangular plate.  Repeat until the table is completed.  Fill in the measured potential difference between the two plates in the last row.

 

Figure 1  Data Table for Potential Difference

Position of COM Probe

Position of VΩ Probe

ΔV (V)

0 (- conductor)

 

1.2

0

 

2.4

0

 

3.6

0

 

4.8

0

20 (+ conductor)

 

 

From the data you recorded in figure 1, record the points you determined between which there is a constant potential difference of 1.2 V.  Fill in the appropriate value for the last row.

 

Figure 2  Data Table for positions Potential Difference steps of 1.2 V

Position Lower Potential Point

Position of Higher Potential Point

ΔV (V)

0 (- conductor)

 

1.2

 

 

1.2

 

 

1.2

 

 

1.2

 

20 (+ conductor)

 

 

Q4)  Do the points between which there is a constant potential difference seem fairly evenly spaced or do they tend to bunch up towards one conductor or the other?  Explain.

 

 

 

Q5)  If the equipotential surfaces are closer together, does that indicate a stronger or weaker field than if they are further apart?  Explain.

 

 

 

4.  Record Equipotential lines

      Use the same procedure as in the previous lab activity to find 4 equipotential surfaces in the region between the plates.  Place the COM probe at the points you recorded in figure 1.  Be sure to include points near the edge of the conductors as well.

 

 

Q6)  On your graph paper, draw electric field vectors along the equipotential surfaces.  Be sure they point in the correct direction and label them with the magnitude of the average electric field.

 

 

 

Replace the circular plate with the triangular plate so that its vertex is along the axis of the graph paper and 20 grids from the inner edge of the rectangular plate.

 

Q7)  You will connect the + terminal of the power supply to the triangular plate and the – terminal to the rectangular plate.  On the figure sketch what you think the electric field lines will look like for this geometry and then sketch what you think the equipotential surfaces will look like.  Use a solid line for the field lines and a dotted line for the equipotential surfaces.

Q8)  Explain your reasoning for your answer to Q7).

 

 

 

 

 

Repeat the series of potential difference measurements that you made above for this geometry.

 

Figure 3  Data Table for Potential Difference

Position of COM Probe

Position of VΩ Probe

ΔV (V)

0 (- conductor)

 

1.2

0

 

2.4

0

 

3.6

0

 

4.8

0

20 (+ conductor)

 

 

From the data you recorded in figure 3, record the points you determined between which there is a constant potential difference of 1.2 V.  Fill in the appropriate value for the last row.

 

Figure 4  Data Table for positions Potential Difference steps of 1.2 V

Position Lower Potential Point

Position of Higher Potential Point

ΔV (V)

0 (- conductor)

 

1.2

 

 

1.2

 

 

1.2

 

 

1.2

 

20 (+ conductor)

 

 

Q9)  Do the points between which there is a constant potential difference seem fairly evenly spaced or do they tend to bunch up towards one conductor or the other?  Explain.

 

 

 

Q10)  Is this effect more pronounced for the circular plate or the triangular plate?

 

 

On the flip side of your graph paper, map out the equipotential surfaces for the points you identified in figure 4.

 

 

Q11)  On your graph paper, draw electric field vectors along the equipotential surfaces.  Be sure they point in the correct direction and label them with the magnitude of the average electric field.

 

 

 

Q12)  Where does the field appear to be strongest?

 

 

 

Q13)  If you have a conductor with a sharp point, how does the strength of the field near the point compare to points near flat places on the conductor?