A thick spherical shell carries charge density k 2 (a b. Plot |E| as a function of r, for the case b = 2a.
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- dx P. ++ + + + + + dq L Evaluate an expression for the electric field at point P of a uniformly charged rod with linear charge density, 2 [C/m²], as shown above. Hint: The integral will be of the form: E (P) = [ k dq , where dq = 1 dx x2 1An infinite, insulating cylinder of radius ri is surrounded by an air gap and a thin, cylindrical conducting shell of radius r2. The insulating cylinder carries constant volume charge density p and the conducting shell carries a constant area charge density o. Use Gauss's law to calculate the quantity f E•dA for the Gaussian shape (a) most appropriate for this problem. (b) distribution). Find the electric field in the region r < ri (inside the volume charge (c) Find the electric field in the region r1 < r < r2 (air gap region) 2.A long hollow insulating cylinder has an inside radius a, outside radius b, and a uniform charge desity ρ. What is the electric field a distance r from the central axis? Give answers for r < a, a < r< b, and r > b
- Imagine that in a region in space you detect a spherical symmetric electric field that increases quadratically with the distance from the center, E (r) = a · r2 . er, where a is a constant. How is the the charge distributed in that region, i.e. find p (r). increases linearly radially outward decreases linearly radially outward uniformA thick spherical shell carries charge density (rho) = k/r^2 for r1 ≤ r ≤ r2. Find the electric field in the three regions: (i) r < r1, (ii) r1< r < r2, (iii) r > r2. Plot the magnitude of E as a function of r, labeling clearly where r1 and r2 are.