Physic II Lab experiment Charges and Fields

M1A1 Experiment: Charges and Fields

PART I - The Electric Field of a Point Charge

· Start the simulation "Charges and Fields" (if you haven't done so already) by clicking on the image below.

http://phet.colorado.edu/sims/charges-and-fields/charges-and-fields_en.html

We are going to take numerical data in this activity, so we need some references points (a coordinate system) and some measuring tools.

· Select the check box for "Grid."

· Select the check box for "Show numbers."

· Select the check box for "Tape measure."

Place a single positive +1 nC charge in the center of the grid. Place an orange E-Field sensor in several locations near, but not on top of, the point charge. Use this sensor to check three properties of the electric field of a point charge.

1. The field is directed radially outward from the charge.

2. The field has a magnitude that is constant for any given radius.

3. The field magnitude at radius r = 2 meters is 4 times that at 4 meters.

While the first two given properties are general, the third property is a specific case of the 1/r² (read as "one over r squared") dependence of the electric field. In other words, the magnitude of the electric field of a point charge drops as the square of the radius. In this activity, you are going to use data to confirm this property. In your favorite spreadsheet program, plot the magnitude of the electric field at 0.5 m intervals. Here ke is the electrostatic constant and is equal to 8.99 x 109 N m2/C2 , and as previously directed, q1 is +1 nC. If your spreadsheet program is capable of doing so, fit a power law curve to your calculated values. In Excel, you can access the dialog box shown below by right clicking on any data point and selecting "insert trendline."

Figure 1: Options for inserting a trendline in Excel showing the 1) power law, 2) display equation options, and 3) the displayed equation

Now within the simulation, take data at intervals other than 0.5 meters. Display both sets of data on a single graph. Do your data points match the calculated curve? How well does your data support the 1/r² dependence of the electric field magnitude on the radius?

PART II -Dipoles and Quadrupoles

The principle of superposition is simply a statement that the electric field at any point is a sum of the contributions to the electric field from individual charges. The electric field is a vector quantity, so this sum requires some vector mathematics.

Figure 2 A dipole consists of equal positive and negative charges (q) separated by some distance (d).

Within the simulation, set up equal positive and negative charges (q) separated by some distance (d). This arrangement of charges is called an electric dipole, and as you might imagine, the resulting electric field is more complicated than that of the point charge. Take a few moments with the simulation, and use an E-Field sensor to explore the shape of the dipole field. Describe your observations in your laboratory notebook. In Figure 2 above, the green line indicates a set of points equidistant from both charges. Describe the magnitude and direction of the electric field along this line. Take the point directly between the two charges as the origin and the green line as the y axis. Calculate the magnitude of the electric field at 0.5 meter intervals along this axis. As with Part I, a spreadsheet program may prove useful. Within the simulation, take data at intervals other than 0.5 meters. Display both set of data on a single graph. Do your data points match the calculated curve? Does the magnitude of the dipole field follow a power law? If so, is it the same or a different power law from that of the point charge? Four Charges: Take four charges and set up a quadrupole field. Here, your origin is the point directly in the center of the charges. Without calculation or graphing, investigate the magnitude of the electric field along the green axis. Compare your observations to the results from the dipole field. What might happen with even larger collections of electrically neutral collections of charges?

Figure 3 Four charges creating a quadrupole field

Solid objects are made up of positive and negative charges in nearly equal numbers. In other words, most large objects are electrically neutral. Like an extreme version of the quadrupole, their electric fields strongly interact on the scale of atoms and molecules, but drop off to negligible levels only a few atomic diameters away. For example, far from the surface of a table the charges that make up my finger feel no net electric field from the atoms in the tabletop. Still, when I bring my finger to within a few atomic diameters of the surface, the electric fields begin to attract or repel depending on the stickiness of my fingers.

Part III - Equipotential Surfaces and Work in the Electric Field

Begin with a single point charge and use the voltage plotting tool to create an equipotential curve around the point charge. Use an orange electric field sensor to investigate the relationship between the direction of the electric field and the orientation of the equipotential curve. Are the two parallel or perpendicular, or do they have some other more complicated relationship? Does this relationship hold for more complicated arrangements of charge, dipoles, and quadrupoles?

Figure 4 Point Charge and the voltage plotting tool.

Recall the definition of work: work = F∙cos(θ)∙Δx. Work can, of course, be done not only by the force of gravity but also by electrical forces. The definition of work done by electrical forces is

Work = (q ∙ E) ∙ cos(θ) ∙ Displacement

Given your observations, speculate on the work required to move a very small test charge along (parallel to) an equipotential line.