HW-11Capacitancedue 10/7/97 HomeworkDeriving a Mathematical Expression for Capacitance You can use Gauss' law and the relationship between potential difference, V, and electric field to derive an expression for the capacitance, C, of a parallel plate capacitor in terms of the area and separation of the aluminum plates.
Derivation of Capacitance vs. A and d Write down the integral form of Gauss' law. Examine the Gaussian surface shown in the diagram above. What is the value of the electric field insidethe top plate? Hint: There is never an electric field inside a conductor when no electric current is present! Using the results above and the notation E to represent the uniform electric field between the two plates, find an expression for the net charge on the top plate, q, in relation to E. Use the relationship between V, E, and d and the definition of capacitance to derive an expression of the capacitnace of a parallel plate capacitor that depends on A , d and k(kappa) where A is the area of the plates, d is their separation and k(kappa) is a quantity called the dielectric constant and is a property of the insulating material that separates the two plates. Use one of your actual areas and spacings from the measurements you made in class to calculate a value of C. How does the calculated value of C compare with the directly measured value? Compare your results to the InfoMall Find two different discussions of capacitance from two different levels of textbooks on the InfoMall. Examine their results for a parallel plate capacitor and for combining capacitors in parallel or in series. Include short quotes from each source and give the complete citation for each reference. Compare your experimental results from class to your readings in the InfoMall. Borrowed by RGF and VPC , at UNL, 10/2/97 from © 1990-93 Dept. of Physics & Astronomy, Dickinson CollegeSupported by FIPSE (U.S. Dept. of Ed.) and NSF