Two coaxial cylindrical conductors are shown in cross-section above. The inner c

Question

Two coaxial cylindrical conductors are shown in cross-section above. The inner cylinder has radius a = 2 cm, length 10 m and caries a total charge of Qinner = + 8 nC (1 nC = 10-9 C). The outer cylinder has an inner radius b = 6 cm, outer radius c = 7 cm, length 10 m and carries a total charge of Qouter = - 16 nC (1 nC = 10-9 C). What is Ex, the x-component of the electric field at point P which is located at the midpoint of the length of the cylinders at a distance r = 4 cm from the origin and makes an angle of 30o with the x-axis?

Ex = N/C

Explanation / Answer

Gauss's law:

E (2r L) = (Qinner)/0

E = (Qinner)/(2r L 0) = (8e-9)/(2*3.1416*0.04*10*8.85e-12) = 359.67 N/C

Ex = E cos30 = 359.67 * 0.86603 = 311 N/C

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