VE230+Homework+3+Fall+2010 - VE 230 Electromagnetics I...

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Unformatted text preview: VE 230 Electromagnetics I VE230 Homework 3 (Due 10/26/10) Fall 2010 3.1 A line charge of uniform density ρl in free space forms a semicircle of radius b. Determine the magnitude and direction of the electric field intensity at the center of the semicircle. 3.2 A horizontal strip lying in the x ­y plane is of width d in the y ­direction and infinitely long in the x ­direction. If the strip is in air and has a uniform charge distribution ρs, use Coulomb’s law to obtain an explicit expression for the electric field at a point P located at a distance h above the centerline of the strip. Extend your result to the special case where d is infinite. 3.3 Two uniform infinite sheets of electric charge densities +ρ and  ­ρ intersect at right angles. Find the magnitude and direction of the electric field everywhere and sketch the lines of E. 3.4 A static electric charge is distributed in a spherical shell of inner radius R1 and outer radius R2. The electric charge density is given by ρ = a + br , where r is the distance from the center, and zero everywhere else. (a) Find an expression for the electric field everywhere in terms of r. € (b) Find an expression for the electric potential. Take the potential to be zero at infinite. 3.5 Determine the work done in carrying a  ­2 µC charge from P1(2,1, ­1) to P2(8,2, ­1) in the field E = xy + yx (a) along the parabola x = 2 y 2 (b) along the straight line joining P1 and P2. € 3.6 A simple classical model of an atom consists of a nucleus of a positive charge € Ne surrounded by a spherical electron cloud of the same total negative charge. (N is the atomic number and e is the magnitude of electronic charge.) An external field E0 will cause the nucleus to be displaced a distance r0 from the center of the electron cloud, thus polarizing the atom. Assuming a uniform charge distribution within the electron cloud of radius b, find r0. 1 ...
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