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Unformatted text preview: Physics 2212 K Quiz #2 Solutions Summer 2009 Permittivity constant m p Mass of a proton Permeability constant m e Mass of an electron e Fundamental charge c Speed of light K Coulomb constant g Acceleration due to gravity Unless otherwise directed, friction, drag, and gravity should be neglected, and all batteries and wires are ideal. Any integrals in free-response problems must be evaluated. I . (24 points) An infinite slab with thickness 2 h has non-uniform vol- ume charge density = z 4 , where is a constant. The slab is infinite in the x and y directions and centered at the origin, ex- tending from- h to + h along the z axis. A finite segment of the slab is illustrated. Find the magnitude of the electric field at a point P located at a position r > + h on the z axis. Express your answer in terms of parameters defined in the problem, and physical or mathematical constants. . . . . . . . . . . . . . . . . . . . . . . . Use Gauss Law. Choose a Gaussian Surface that has a top and bottom parallel to the xy plane, and has sides parallel to the z axis, such as a cylinder. Let it extend from z =- r to z = + r . (Note that due to the symmetry of the charge distribution, the problem could be solved with a Gaussian Surface that extends from z = 0 to z = + r .) Let the area of the Gaussian Surfaces top and bottom each be A . Then E = q in where E = I ~ E d ~ A = E 2 A since, from the symmetry of the charge distribution, the electric field is parallel to the area vectors at both the top and bottom, and perpendicular to the area vectors on the sides. The charge inside the Gaussian Surface must be found by integration, since the volume charge density is not uniform. The charge density varies in the z direction, so choose a volume element that is small in that direction, such as a thin disk with area A and thickness dz ....
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