Question

A charged disk and a charged ring are centered at the origin in the free space as shown in figure 4. Bothe changed elements exists in the xy plane. The disk has a radius a and carries a uniform surface charge density of Ps. The ring has a radius 2a and carries a uniform line charge density Pe. Find the following: a) The electric field intensity on z-axis and determine where the electric field is zero b) The electric potential any point on the Z-axis. c) The force developed on charge of 2nC when it is placed at the point (O, 0, 1) d) The total charge on the ring and on the disk.

Answer 1

Formula for Disk: f_z_1 = p_s/4 pi E-0 2 pi [1 - z/sq z^2 + a^2] k^^formula for ring: f_z_2 = -rho times 2pi times 2a times z/4 pi E_0 [z^2 + (2a)^2]^3/2 k^^rightarrow E_z_1 + E_z_2 E_z = -rho_l times 8 pi a z/4 pi E_0[z^2 + (2a)^2]^3/2 k^^+ rho_s 2 pi/4 pi E_0 [1 - z/squareroot z^2 + a^2] k^^E_z = 1/2 E_0 = [rho_s [1 - z/squareroot z^2 + a^2] - rho_l times 4az/(z^3 + 4 a^2)^3/2] k^^E_z = 1/2 E_0 [rho_s squareroot z^2 + a^2 - z rho_s/squareroot z^2 n + a^2 - rho_l times 4az/(z^2 + 4a^2)^3/2] k^^ \r\n for E_z = 0 put the value of the constant and solve for E_z = 0 v_z due to disk v_z_1 = 1/4 pi E_0 rho_s times 2pi [squareroot z^2 + a^2 - z]