Question

1Introduction Computer equipments, x-ray machines, medical diagnosis equipments and many other industrial equipment are designed using electrostatic field theory. The theory uses essential mathematical tools such Since real life engineering applications involve 3D geometries whose fields are as vector calculus. functions of space (and time), it is critical that you master these tools. In real life, equipment/devices are not restricted to rectangular/cubical geometries but may be of cylindrical/spherical shapes. Objective: For a given scalar potential distribution inside a region, it is required to calculate the corresponding vector electric field, charge density and total charge enclosed 2 Tools and Background It is recommended that you read textbook materials. Search the Internet and/or Library for the proper vector calculus expressions in Cylindrical and Spherical Coordinates: the gradient, the divergence and triple integrals. 3 Questions Find a) The electric flux density vector: D =-e VV, where e is a constant = 10 pF/m. b) The electric volume charge density at any point in the region: p, = V»D = divergence of D c) The total charge enclosed by the specified region: Q = P,dv, dv= element of volume d) Find Vx D and show that D is irrotational. In the cylindrical region: 0sr< 2m, 0<0<n / 2, 0sz<lm, the potential field V is given by V = 50 r2 sin0 volts Your report should include A) A covering sheet indicating title of project, your name, id#, and section, B) Detail derivation for the above questions (four parts) with proper captions, C) Comments on your results, if any.

Answer 1

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