Question

P's The diagram above shows a cross-section view of a very long straight metal cylinder of radius ri within a coaxial hollow metal cylinder of inner radius r2 and outer radius r3. The inner cylinder has a positive charge per unit length λ, whereas the outer cylinder has negative charge per unit length There are no other objects nearby Part A (a) What is the shape of the electric field in and around the cylinders? In your answer (i) explain why, in electrostatic equilibrium, the electric field within each metal cylinder (re- gions A and C) is zero; (ii) explain why any electric field in regions B and D must be radially symmetric; and (iii) illustrate the shape of the field by drawing electric field vectors or field lines (b) Derive from first principles an expression for the electric field magnitude in regions B and D as a function of the distance r from the centre. Your answer should be in terms of the linear charge density, the relevant radii and the electrostatic constant (c) Sketch the electric field magnitude as a function of the distance r from the centre of the cylinders Is the dependence on r far away from the cylinders as you expect? Explain Part B (Advanced) (a) Using the results of Part A, or from first principles, derive an expression for the potential difference between the inner and outer cylinder:s (b) Suppose that a hollow neutral metal cylinder is placed around the inner cylinder but within the other one (without touching either). Would the potential difference between the inner and out cylinders increase, decrease, or stay the same? Explain

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