Part 1) A very long straight wire has a uniform charge per unit length A (upper case "Lambda"). Considering a cylindrical Gaussian surface, or otherwise, give an expression for the electric field at a perpendicular distance r from the wire. (Use the permittivity 6'0, not Coulomb's constant k). E= Figure 1. Three long parallel wires of length L and mass m sit at the corners of an equilateral triangle with side length a. The two base wires are fixed on the ground. Three very long wires all have the same length L, mass m and uniform charge per unit length A (upper case "Lambda"). Two are fixed on the ground, a distance a apart at a place where the acceleration due to gravity is g. The value of A is adjusted so that, with their ends all lying in the same normal plane as shown, the system is in mechanical equilibrium, with three equal separations a. Part 2) Consider the position of the top of the wire when the spacing is a, as shown. Give an expression for the magnitude of the electric field due to the two lower wires. Evaluate any trigonometric expressions in your answer exactly (as surds). E= Part 3) For the condition of mechanical equilibrium of the top wire, give an equation relating a to the uniform charge per unit length A to the other variables in this problem. Evaluate any trigonometric expressions in your answer exactly (as surds). a=