# hw4sols - MasteringPhysics 1:47 PM Assignment Display Mode...

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2/27/08 1:47 PM MasteringPhysics Page 1 of 6 http://session.masteringphysics.com/myct Assignment Display Mode: View Printable Answers Physics 202 Assignment 4 Due at 11:00pm on Wednesday, February 20, 2008 View Grading Details Potential Difference and Electric-Field Energy of a Spherical Capacitor Description: Calculate the potential difference and the electric-field energy of a spherical capacitor. A spherical capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 10.0 centimeters, and the separation between the spheres is 1.50 centimeters. The magnitude of the charge on each sphere is 3.30 nanocoulombs. Part A What is the magnitude of the potential difference between the two spheres? Hint A.1 How to approach the problem Find an appropriate Gaussian surface for the system; then use Gauss's law to calculate the electric field between the concentric spheres. Use the calculated electric field to find the potential difference between the spheres. Hint A.2 Choosing the Gaussian surface Because of the spherical symmetry of the spherical capacitor, the best Gaussian surface to use for this system is a sphere with radius that satisfies the criterion , where is the radius of the inner sphere and is the radius of the outer sphere. Part A.3 Find the electric field Find an expression for the magnitude of the electric field on the Gaussian surface. Note that the spherical symmetry of the situation ensures that the electric field will have constant magnitude over a particular spherical surface. Part A.3.a Calculate the integral in Gauss's law Gauss's law states that . Using a sphere of radius as a Gaussian surface, evaluate the integral on the left-hand side of the equation. Hint A.3.a.i Direction of the electric field By symmetry, the electric field points radially at all points between the spheres, so for any surface element on the Gaussian surface, the normal of the surface element will be parallel to the electric field at all points, so . Express your answer in terms of the magnitude of the field and the radius of the Gaussian surface. ANSWER: = Express your answer in terms of some or all of the following variables: the radius of the Gaussian surface, the permittivity of free space , and the magnitude of the charge on the inner sphere. [ Print ]

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2/27/08 1:47 PM MasteringPhysics Page 2 of 6 http://session.masteringphysics.com/myct ANSWER: = Note that if the inner sphere is negatively charged, the electric field will point inward instead of outward, but it will still be pointing radially. Hint A.4 How to use the electric field to calculate the potential difference To calculate the potential difference, use the equation . If a radial path is chosen to go from the inner sphere to the outer sphere, then the electric field and the path will be parallel, and therefore . ANSWER:
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hw4sols - MasteringPhysics 1:47 PM Assignment Display Mode...

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