Lab Activity: EM Fields Names: ________________
Exploring Electric Potentials & Electric Fields
Introduction & Objectives:
In this lab activity we will use the EM Field simulation software in our physics lab to visually explore the nature of electric potentials and electric fields. We will determine the electric field from an understanding of the electric potential. But we could just as well go the other direction.
In one dimension, the electric field is the negative derivative of the electric potential with respect to position:
E x
  dV dx
The fundamental theorem of calculus tells us that by using integration we can go from the electric field back to the electric potential.

Edx
Our objective in this activity is to use the EM Field software to determine shapes, magnitudes and superposition of equipotentials. Then we'll study how equipotentials can give valuable information on the magnitude and direction of the electric field.
Electric Potential & Equipotentials:
 Electric potential is a scalar quantity.
 The value of the electric potential at a position near a charged particle or object gives a relative value for the electrical potential energy per unit charge at that position: V

U el q
 The units for electric potential are then "energy/charge" or in the MKS system:
Joule/Coulomb = Volt, or 1 J/C = 1V.
 When you go hiking in the mountains and you decide where to put your boot next you can choose a point that is higher, lower, or at the same altitude. There will most likely exist a point with the same altitude. You could theoretically always stay at the same altitude, i.e. you can form a contour map of points with the same altitude, or an equipotential. Similarly, there exist points near a charged object that have the same electric potential. The locus of these points of same electric potential, or equipotential form a curve or surface surrounding the charged object that looks like a halo. The simulation program is two-dimensional and draws equipotentials as you use the mouse to click at points in the region surrounding the charges. The equipotential curves describe the electrical potential landscape near the charges in the same way that a topological map describes the gravitational potential landscape. Disclaimer: technically, altitude above sea level is not a perfect measure of the gravitational potential because Earth is not homogeneous in its mass distribution but it is a very good approximation.
1. Note on units: the software does not directly use volts and meters as units. Distances are measured in gridpoints, k=1 (not 9x10 9 Nm 2 /C 2 ), and charge is measured in increments of +1 or -1 (no Coulomb).
2. Typically, in a representation of an electric field with field lines the density of field line s represents the magnitude of the field. With our EM field software we get a field line wherever and whenever we click. Thus the density of field lines in our case depends on clicking and has no other meaning. Similarly, a representation of an electric field with equipotentials typically plots equipotentials in equal increments (e.g. -5V, 0, 5V, 10V etc), and therefore the spacing

Lab Activity: EM Fields Names: ________________ of equipotentials typically gives us information on the electric field. For the same reason as above, this is not true for EM field software.

Lab Activity: EM Fields Names: ________________
Part I: Equipotentials of a Point of Charge
Procedure:
A. Use EM Field to set up a positive +3 point charge on a grid point near the center of the screen. Include the grid.
Under the "Sources" menu select "3D Point Charges"
Under the "Display" menu select "Show grid"
Click and drag a +3 positive charge to a grid point near the center of the screen.
B. Under the "Field & Potential" menu select "Equipotential with Number".
Click on grid points along a horizontal line going through the charge to display the shape and value of the equipotentials in the region of the charge. Do this for a few points until you feel the equipotentials help you adequately visualize the field.
C. Use “ctrl” + “Print Screen” to copy and then paste the picture of the screen into a word document. Save your data to a disk.
Exercises & Questions:
1. Dependence of Electric Potential on Distance from the Charge:
Use your saved picture of the screen to create a graph of electric potential vs. distance from the charge (e.g. in Excel). Describe the nature of the relationship between electric potential and distance from the charge.
2. Dependence of Equipotentials on Magnitude & Sign of Charge:
Predict what changes in the equipotential lines might occur if the magnitude of the charge is changed. What if the sign of the charge changes? Test your predictions using
EM Field and copy & paste the results into your word document. Write a discussion of your results. Refer to saved copies of your results in your discussion.

Lab Activity: EM Fields Names: ________________
Part II: Superposition of
Equipotentials
Procedure:
A. Use the saved equipotential maps of the positive and negative equal magnitude charges that you were asked to create in Part I.
B. Use the data gathered for these charges to calculate the magnitude of the electric potentials at grid points along a horizontal axis running through the two charges if they were positioned as a dipole with four grid points as shown in the figure above. Show how you made these calculations.
C. Make a prediction sketch of the equipotentials for this dipole charge distribution.
D. Show your predictions to your instructor before you use EM field to test them.
E. Use EM Field to set up the dipole situation described above of two equal and opposite charges on the screen with 4 grid points between them. The charges should have the same magnitude those you used in the previous steps.
E. Click on grid points along a horizontal axis running through the two charges to display the shape and value of the equipotentials in the region of the charges.
F. Copy and paste your results to your word document.
Exercises & Questions:
1. Compare your predictions and observations from the previous exercise. Did your calculated potentials agree with your observations? Did the shape of your predicted equipotentials agree with your observations?
2. If you were to calculate the potential field for a continuous charge distribution, how would your method differ from what you did for E-field integrations?
3. Predict the equipotential landscape for two charges of like sign and magnitude.
Draw the picture and calculate the potential along the line connecting the two charges (as you did above for the dipole). In your report, include the prediction here (hit return to create space)
4. Check your prediction using EM field and discuss.

Lab Activity: EM Fields Names: ________________
Electric Fields & Electric Field Lines
Definition:
As described in the introduction, an electric field can be determined from the electric potential by taking the derivative of the potential with respect to position. More precisely, the electric field is defined as the negative gradient of the electric potential which for rectangular symmetries would be calculated:
E x
  dV dx
E y
  dV dy
E z
  dV dz
OR
E r
  dV dr for spherical symmetries.
Electric Fields:
1. The electric field is a vector quantity.
2. It describes the magnitude and direction of the electric force per unit charge at some position.
3. The units of the electric field are "Force/Charge" or in SI: N/C.
4. The electric field gives the magnitude and direction of maximum change in the electric potential. For example, the electric field will not be directed parallel to an equipotential line because by definition the electric potential is not changing along this line.
We will use EM Field to show that the electric field of a charged object can be easily determined if the equipotential lines are already known for the object. In exploring the connection between electric fields and electric potentials it can be helpful the keep in mind the analogous relationship that exists between gravitational potential and gravitational force.

Lab Activity: EM Fields Names: ________________
4.
Part III: Electric Fields & Electric Field Lines - Point Charge
A. Use EM Field to set up a positive +3 point charge on a grid point near the center of the screen. Include the grid.
B. Under the "Field & Potential" menu select "Equipotential with Number". Click on grid points along a horizontal line going through the charge to display the shape and value of the equipotentials in the region of the charge.
C. Under the "Field & Potential" menu select "Field Vector". Click on grid points along a horizontal line going through the charge to display the electric field vectors in the region of the charge.
D. Under the "Field & Potential" menu select "Field Lines". Click on grid points around the charge to display the electric field lines in the region of the charge.
E. Copy and paste your data to a word document.
Exercises & Questions:
1. Dependence of Electric Field E on Distance from the Charge:
Use your saved picture of the screen to create a graph of electric field E vs. distance from the charge (e.g. in Excel). Describe the nature of the relationship between E and r.
How does it compare to the relationship between electric potential V and r that you discovered in Part I?
2. Relationship between the electric field and the electric potential:
The magnitude of the electric field can be approximated by calculating how the electric potential is changing from one position to another. Using the printout of the potential data you've collected, calculate for every grid point the electric field:
E =

V/
 x = (V2 - V1) /
 x
Create a graph of the values (E vs. x) and compare your result to the graph you created directly above in #1. Note on units: EM field is dimensionless, i.e. doesn’t use units.
We’ll cheat a bit here and will use V(olt) for potential and assume grid points are 1 cm apart.
3. Electric field lines and equipotential lines:
Discuss the equipotential lines are oriented with respect to electric field lines? Do not yet discuss the magnitude of E along an equipotential (we are looking at a very special example here that would give you the wrong idea if you did).
Dependence of Electric Fields on Magnitude & Sign of Charge:
Predict: how would E change if the magnitude of the charge is changed?
Predict: how would E change if the sign of the charge is changed?
Test your predictions.
Copy and paste your results to your word document and discuss.

Lab Activity: EM Fields Names: ________________
B.
Part IV: Exploration of Complicated Charge Distributions
Procedure:
A. Use EM field to create maps showing the electric field lines and equipotentials for the following charge distributions: i. ii. iii. iv. equal and opposite charges - electric dipole. two equal charges. two charges - one very negative and the other slightly positive. four equal charges positioned at the corners of square.
Keep the charges fairly close together on the screen so that you can see their effect on the space surrounding them as well as between them. Especially for iii & iv test areas close to the charges and at the edges of the screen. Take time to create complete maps.
Copy and paste your data to your word document.
Exercises & Questions:
1. What can you say about the orientation of the electric field and an equipotential?
2. If the electric potential is zero, is the electric field also zero?
3. In general, along an equipotential, is the electric field constant in magnitude?