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Suppose a stream of negatively charged powder is blown through a cylindrical pipe of radius R.Assume that the powder and its charge are spread uniformly through the pipe with a volume charge density ?.a) Find an expression for the magnitude of the electric field in the pipe, as a function of radial distance r from the pipe center. Include a drawing labeled with R, r, and any other relevant quantities.b) Does the magnitude of E in the pipe increase or decrease with increasing r? Sketch a graph of its behavior as a function of r, from 0 to R.c) Is E in the pipe directed radially inward or outward?d) If the pipe had radius R = 5.0 cm and the volume charge density in the powder was3 ?=1.1*10^-3C/m^3 (a typical value at the factory), find the maximum value of E occurring in the pipe.e) Could sparking occur in the pipe with the values given in d), and if so, where would it occur?
