Question

An infinite sheet of charge that has a surface charge density of 23.4nC/m^2 lies in the yz plane, at x=0. A long wire having a linear charge density of 79.7nC/m lies parallel to the y axis and intersects the x axis at x = 2.85m. The potential at the origin is 1.44kV. Determine, the potential on the x axis at x-0.797m, between the wire and the sheet. Submit Answer Tries o/10

Answer 1

Surface charge density of sheet, sigma = 23.4 times 10^- 9 c/m^2 lineal charge density of course, lambda = 79.7 times 10^- 9 c/m Intersect at x = 2.85 m potential at origin, V = 1.44 kV V_x = 0.797 m = ? E_sheet = sigma/2 epsilon_0 E_line = lambda/2 pi epsilon_0 (x - d) i^V = V-0 - integral^x_0 [E_sheet + E_line] dx = V_0 - sigma x_0/2 epsilon_0 - lambda/2 pi epsilon_0 ln (d - x_0/s) = 1440 V - 23.4 times 10^- 9 times 0.979/2 times 8.854 times 1512 - 79.7 times 10^- 9/2 pi (8.854 times 10^- 12) ln (2.85 - 0.797/2.85) = 1440 - 1053.185 + 469.932 potential = 856.75 V