Question

17. The axis of a long hollow cylindrical shell of radius 2 cm coincides with a long wire. The wire has a linear charge density of 8.85 pC/m, and the cylinder has a net charge per unit area of 8.85 pC/m2. Determine the magnitude of the electric field 5 cm from the axis A) 5.97 V/m B) 4.48 V/nm C) 3.58 V/m D) 2.98 V/m E) 2.24 V/m

Answer 1

Electric field of line charge (wire) at 5cm is E_1 = lambda/2 pi epsilon_0 z q/L = lambda = 8.85 times 10^-12 c/m E = 8.85 times 10^-12/2 times pi times 8.85 times 10^-12 times 5 times 10^-12 = 1/pi times 10^-4 = 3.1847 v/m \r\n electric field at 5 cm due to hollow cylinder E_2 = lambda/2 pi epsilon_0 z but given sigma = 8.85 times 10^-12 doublerightarrow q/2 pi R L = 8.85 times 10^-12 = q/L = 8.85 times 10^-12 times 2 pi R doublerightarrow lambda = 8.85 times 10^-12 times 2 pi R doublerightarrow E_2 = 8.85 times 10^-12 times 2 pi R/2 pi epsilon_0 z = 8.85 times 10^-12 times R/8.85 times 10^-12 times 2 = 2 times 10^-12/5 times 10^-12 = 2/5 = 0.4 v/m total field = E = E_1 + E_2 = 3.1847 + 0.4 = 3.5847 v/m