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A coaxial cable has a thin conducting copper wire at the centre of the cable, positively charged with linear charge density 2= 8.0 x 10⁹ C/m. It has a rubber coating (dielectric constant & = 2.7, relative permeability = 3.9) of inner radius a = 0.4 mm and outer radius b = 0.9 mm, and an air gap exist between the core wire and the rubber coating. (see Figure 1). D λ (C/m) Rubber- L Figure 1. Coaxial copper cable geometry (a). Calculate the electric field magnitude (with correct unit) at radial distance from the copper wire r = 0.2 mm (air). Use three significant figures. [2] (b). Calculate the electric field magnitude (with correct unit) at radial distance from the copper wire r = 0.7 mm (rubber). Use three significant figures. [2] (c). Calculate the electric field magnitude (with correct unit) at radial distance from the copper wire r = 1.3 mm (air). Use three significant figures. [2] (d). Plot the magnitude of the E field E(r) with respect to r, from 0 to r = 1.3 mm, specifying all the discontinuities. [4] (e). Based on the results in (d), plot a qualitative potential function V(r) with respect to r, from r = 0.2 mm to r= 1.3 mm, with reference 0 V at r=1.3 mm, i.e., V(r=1.3 mm) = 0. [4]