Overview
Purpose
If you have a set of points that are all at the same potential these are called equipotentials and a line connecting a set of equipotential points is called an equipotential line. In this lab we will map these lines for different charge distributions. The following equations may be useful where s is a dummy variable (meaning it can be x, y, z, etc), E is the electric field, and V is the voltage:
𝐸→=−𝑑𝑉𝑑𝑠𝑠^
or
𝐸→=−∇𝑉
meaning the three dimensional derivative that gives you the path of steepest descent.
By the end of this lab you should be able to: • Have an intuitive understanding of electric potentials and fields for some basic charge distributions. • Determine the relationship between electric field and electric potential. Materials/Equipment Charges and Fields Phet Simulation https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_en.htmlLinks to an external site.
Setup 1. Open the simulation. 2. Uncheck all the options except gridlines. 3. Know where the voltage meter and ruler are.
Flag question: Question 1Question 15 pts
Map the equipotential lines and electric field lines TWO LINES PROCEDURE 1. Draw two straight lines out of charges on the grid spaced about 3 meters apart.
[Image unavailable: Set up for charge lines.]
Check the voltages on the blue charge line and the red charge line
On graph paper or a screenshot of your image, plot lines of equal voltage (equipotential lines) by using the voltage probe to trace a line where the voltage is the same along the line. Do this by moving the mobile probe along the grid until you find a point where the multimeter reads 0.0 V. The point will not necessarily be right at one of the grid markings.
Note: it can be hard to get exact values. Do the best you can. The point here is to find the pattern.
Repeat until you feel confident you have mapped out all the points on the grid that are at 0.0 V; then draw a line connecting these points. As the pattern develops, you may find it easier to anticipate where the points will fall. Be sure to check over the entire grid, however, including behind and to the side of the electrodes. Label the line “0.0 V.”
Repeat the above procedure to map at least 6 more lines of varying voltages between the values you read off the blue and red charge lines.
Represent the electric field lines (NOT VECTORS) by drawing 8-10 equally spaced, continuous lines which are everywhere perpendicular to the equipotential lines. Draw arrows on the field lines indicating the direction of the electric field. Use a different color from the color used to map the equipotential lines.
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Flag question: Question 2Question 26 pts
Two Lines
A. Where are the electric field lines closest together?
B. What is the approximate potential midway between the two conductors?
C. What, approximately, is the strength of the electric field midway between the two conductors? Hint: You will need the voltage difference between two lines near the center and their distance apart. Calculate first, showing your work, then use a sensor to check.
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TWO CIRCLES Repeat the mapping for the sheet with two circles. Draw an evenly spaced positive and negative ring in your simulation and repeat the procedure from the previous section.
[Image unavailable: Rings of Charge set up.]
Represent the electric field lines by drawing 8-10 equally spaced, continuous lines which are everywhere perpendicular to the equipotential lines. Draw arrows on the field lines indicating the direction of the electric field. Use a different color from the color used to map the equipotential lines.
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Flag question: Question 4Question 44 pts
Two Circles
A. What is the approximate potential midway between the two conductors?
B. What, approximately, is the strength of the electric field midway between the two conductors? Hint: You will need the voltage difference between two lines near the center and their distance apart.
You may find it easier to answer this question if you just measure the potential at a few points near the center. Calculate first, showing your work, then use a sensor to check.
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RANDOM SHAPE Repeat the mapping for a third, different pattern with two random shapes.
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Flag question: Question 6Question 65 pts
Conclusions
A. What changes if you switch which side is red (positive) and which is blue (negative)?
B. If you wanted to push a charge along one of the field lines from one conductor to the other, how does the choice of field line affect the amount of work required? (Think carefully about work and how it relates to potential and potential energy.)
C. The potential is everywhere the same on an equipotential line. Is the electric field everywhere the same on an electric field line?
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