Charged disk – symbolic and analytical solutions. Consider a very thin charged disk (i.e...

Charged disk – symbolic and analytical solutions. Consider a very thin charged disk (i.e., a circular sheet of charge), of radius a and a uniform surface charge density ρ_s, in free space, and the electric field it generates at a point P along the z-axis in Fig.1.8 (a). By subdividing the disk into elemental rings of width d_r, as shown in Fig.1.8 (a),

applying Eq.(1.15) for the field at the point P due to a ring of radius r (0 ≤ r ≤ a) and charge being the surface area of the ring (calculated as the area of a thin strip of length equal to the ring circumference, 2_πr, and width d_r), and superposition, the total electric field vector is given by

Using this expression and function integral (written in the previous MATLAB exercise), compute E by symbolic integration. Also, solve the integral analytically and plot both solutions for ρ_s = 2 mC/m², a = 10 cm, and −2a ≤ z ≤ 2a. (ME1 11.m on IR)

Reference: Equation (1.15)