Lab Simulation #4 Name: _________________________________

𝑬-FIELD LINES, & EQUIPOTENTIAL SURFACES VIRTUAL LAB

We can represent the scalar function of the electric potential graphically by drawing equipotential lines (in two dimensions) or equipotential surfaces (in three dimensions). Believe it or not, you have already constructed these three-dimensional equipotential surfaces in the last unit: Gaussian surfaces. Remember, the Gaussian surfaces were drawn as to have a differential area vector 𝑑𝐴 which aligned with the electric field (so the surface was perpendicular to the direction of the field). The definition for the electrical potential difference between two points

ΔV =Vb −Va =!E ⋅d!ℓ

a

b

∫

shows the vector dot product in the integrand refers to a path traveled in the electric field. In order for a field to do work on a charged object, the dot product with the field (force per charge) cannot vanish; thus, a path taken perpendicular to the direction of the field results in no change in electrical potential difference (or electrical potential energy).

Procedure 1. Navigate to PhET Interactive Simulations webpage, and select Charges and Fields:

https://phet.colorado.edu/en/simulation/charges-and-fields Your score on this laboratory simulation will be based on the completeness and accuracy of the graphs. To assist you in understanding how to use the simulation, watch this ScreenCast.

Charge Distribution Set-Up 2. Beginning with a blank canvas, un-click the checkbox for Electric Field to avoid a cluttered screen. Click the

checkbox to show the Grid and Values (which shows you the major gridlines are 50 cm apart). Drag charges from the bottom menu, and stack them directly on top of each other until you’ve reached the desired value; for example, to achieve the desired charge distribution shown in arrangement #1: stack 2 “+1 nC” charges exactly on top of each other on the left, and two “‒1 nC” charges exactly on top of each other on the right. Use the gridlines to assist you.

Equipotential Values and Equipotential Surfaces You will be using the equipotential finder tool (shown on the right) to generate information for *both* graphs: (1) record the value of the electric potential value at the location of the surface to generate the points for the graph of electric potential vs. charge location, and (2) draw the corresponding equipotential surfaces exactly as you see them on the simulation screen (in size, shape, and scale). 3. Click and drag over the blue equipotential finder tool (voltage finder) icon. To use the tool, you place the crosshairs

at the location where you wish to determine the voltage. In the analysis portion for this activity, will be creating graphs of Electric Potential versus Charge Location; therefore, we must first determine the minimum and maximum voltage values for the charge arrangement. Place the crosshairs of the Equipotential icon very close to the edge (but not on) each charge. For example, arrangement #1 has a maximum voltage of about +200 V (where the crosshairs of the sensor are placed at the edge of the +2 nC charge) and a minimum voltage of about ‒200 V (where the crosshairs of the sensor are placed at the edge of the ‒2 nC charge).

4. Divide this voltage span into equal segments and populate the Electric Potential (vertical) axis with these divisions. For example, since arrangement #1 has a voltage span of about 400 V, we could create eight equally-spaced voltage increments along the vertical axis: ‒200 V, ‒150 V, ‒100 V, ‒50 V, 0 V, 50 V, 100 V, 150 V, 200 V.

5. Once these voltage divisions have been determined, use the equipotential finder tool to determine these voltage values along the horizontal line shown. Once the voltage has been located, click on the pencil icon to draw the equipotential line at that location. Create a data table to record both the Location (symmetrically along the axis shown connecting the charges) and the Voltage for each of the voltage increments you determined in the previous step. Click on the Tape Measure icon to help you determine the locations accurately.

Electric Field and Equipotential Lines 6. On the lower graph, you are to show the equipotential surfaces and the electric field lines. Using the same scale as

in the simulation, carefully draw each of the equipotential lines (the same lines used to create the graph of electric potential versus charge location).

7. On the graph of the equipotential surfaces, now carefully draw the electric field lines. To assist you in drawing in the electric field lines, you may click the checkbox to display the Electric Field. The direction of the electric field at a specific location is shown by the direction of the arrow at that location, and the magnitude is represented as the boldness of the color of the arrow. Remember, equipotential lines intersect the electric field lines perpendicularly.

Charge Arrangement #1: *ScreenCast* Two Positive Points Charges of Unequal Magnitude

Use this ScreenCast to assist you in beginning the work for this charge arrangement. Complete the work for this charge arrangement and for the other two charge arrangements that follow. A Graph of Electric Potential vs. Charge Location:

Electric Field Lines and Corresponding Equipotential Surfaces:

Location Voltage

Charge Arrangement #2: Symmetric Electric Dipole A Graph of Electric Potential vs. Charge Location:

Electric Field Lines and Corresponding Equipotential Surfaces:

Location Voltage

Charge Arrangement #3: Two Lines of Equal and Opposite Charge A Graph of Electric Potential vs. Charge Location:

Electric Field Lines and Corresponding Equipotential Surfaces:

Location Voltage