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?

Explanation / Answer

1. The problem statement, all variables and given/known data Two coaxial cylindrical conductors are shown in perspective and cross-section above. The inner cylinder has radius a = 2 cm, length L = 10 m and carries 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 L = 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? 2. Relevant equations E?dA=qenclosed/e 3. The attempt at a solution Okay so I found the charge per unit length (?) which is Lguasss. ?=0.8 nC. Then I performed the integral and solved for E to get E=qenclo/(2*Pi*e*r*L). I wasn't sure how to get the x component though but figured it must be just E mag * Cos[theta] but this is wrong. Can anyone help me? I hope I showed enough work to get a response. I can double check my units and everything but I am pretty sure I converted everything to the proper units.

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