1 a long rod made from non conducting material is charged with a total

Question

1. A long rod made from non-conducting material is charged with a total of 1 Coulombs per metre. The rod has a circular cross-section of radius R. The arrangement of charge in the rod is such that the charge density p(r,0,z) depends only upon r, i.e.it is radially symmetric and independent of z. Furthermore,the charge density varies linearly with distance from the central axis of the rod and is zero at the outer surface. a. Show that the charge density is \rho(r)=\frac{3 \lambda}{\pi R^{3}}(R-r) b. Taking the electrostatic potential to be zero at r = 0,determine an expression for the electrostatic potential as a function of r for \text { i. } 0 \leq r<R \text { ii. } r \geq R . Plot or sketch a graph showing the radial variation of the electrostatic potential over the range 0 <r<2R. d. Describe and comment upon what happens to the electrostatic potential as r → ∞.