Question

The cross section of a 1-m long coaxial cable is shown in the figure, with radii as given. The charge on the inner conductor is -30 nC and the charge on the outer conductor is -70 nC. The inner and outer cylindrical surfaces are respectively denoted by A, B, C, and D, as shown. $9k=$

(a) The radial component of the electric field at a point that 34 mm from the axis is?

(b) The radial component of the electric field at a point that 94 mm from the axis is?

Answer 1

The linear charge density on inner conductor lambda_1 = -30 nc = -30 times 10^-9 c The point which is at distance r = 34 mm from the center of inner conductor lies in region B and C According to Gauss law Electric field due to cylinder E = lambda_1/2 pi epsilon_0 r Here epsilon_0 = 8.85 times 10^-12 c^2/Nm^2 lambda_1 = -30 times 10^-9 c r = 34 mm = 34 times 10^-3 m Putting all these values in the formula: E = -30 times 10^-9/2 times 3.14 times 8.85 times 10^-12 times 34 times 10^-3 = -30 times 10^-9 + 12 + 3/1889.652 = -30 times 10^6/1889.652 E = -15875.93 N/c \r\n Linear charge density on inner conductor = lambda_1 = -30 nc = -30 times 10^-9 c linear charge density on out conductor = lambda_2 = -70 nc = -70 times 10^-9 c