A rectangular beam is subjected to a uniformly distributed load of $10$ kN$/$m over a span of $4$ meters. The beam has a width of $200$ mm and a depth of $300$ mm$.$ Calculate the maximum bending moment experienced by the beam and determine the maximum stress induced in the beam material. Assume the beam is made of a material with a modulus of elasticity $($E$)$ of $200$ GPa.