Go to https://www.compadre.org/Physlets/electromagnetism/intro24.cfm. In the next set of activities you will see how Gauss's law can be

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Go to https://www.compadre.org/Physlets/electromagnetism/intro24.cfm. In the next set of activities you will see how Gauss's law can be used to find unknown charges. Open Exploration 24.1. The simulation shows the electric field of a charge and three different Gaussian surfaces that can be used to detect the field. Note that the circular surfaces shown are actually cross sections of complete spheres in three-dimensional space. A red test charge is also shown. The electric field value given in the simulation is the value of the electric field at the location of the test charge, which is listed at the bottom left of the simulation window.

2. Click on the test charge and drag it along each of the Gaussian surfaces. Take care to make sure that the charge is right on the surface so that you get good measurements. Record the radius of each sphere and the value of the electric field at the location of each of the Guassian surfaces. Be sure to include units. Rgreen = _____________ Egreen = _______________ Rred = _____________ Ered = ________________ Rblue = _____________ Eblue = ________________

3. What is the direction of the electric field at the location of each of the surfaces?

4. What is the direction of the normal to the Gaussian surfaces relative to the electric field direction in each case?

5. If the electric field and the normal are at all points parallel to each other, the integral for determining the electric flux can be significantly simplified: E dA E dA EA cos cos cos . What is the angle between the area vector and the electric field in each of the three boxes above?

6. Use the expression above and the known angle to calculate the flux through each of the three Gaussian surfaces. Show your work, and be sure to include units. Remember that the surface area of a sphere is 2 A r 4 . green = ______________ red = _______________ blue = _______________

7. How do the values of the flux for the three surfaces compare? Does the value of the flux depend on the area of the Gaussian surface? Why or why not?

8. According to Gauss's law, the amount of flux through a closed surface depends only on the charge enclosed by that surface. Use Gauss's law and your measurements to determine the magnitude and sign of the charge shown in the simulation. Show your work and be sure to include units.