The cross section of a long coaxial cable is shown in the figure, with radii as given. The linear charge density on the inner conductor is -30 nC/m and the linear charge density on the outer conductor is -70 nC/m. The inner and outer cylindrical surfaces are respectively denoted by A, B, C, and D, as shown. (ε0 = 8.85 × 10^-12C²/N ∙ m²) The radial component of the electric field at a point that 34 mm from the axis is closest to

Question

Quizplus · Accepted Answer

Using Gauss's Law, we can find the electric field at a radius of 34 mm as follows:

- Draw a Gaussian cylinder with radius 0.034 m and length L such that it intersects with both conductors.
- The electric field is radial, so we choose the Gaussian cylinder to have a circular cross section, which simplifies our calculation.
- By symmetry, the electric field is constant along the surface of the Gaussian cylinder, denoted as E.
- The electric flux through the curved surface of the cylinder is zero since the electric field is perpendicular to it.
- The electric flux through the top and bottom surfaces of the cylinder add up to the total charge enclosed by the cylinder divided by ε0.
- The linear charge densities on the inner and outer conductors give us the total charge enclosed as -(30 × 10^-9 × π × (0.014^2 - 0.008^2) - 70 × 10^-9 × π × (0.034^2 - 0.014^2)) × L.
- Equating those two expressions and solving for E, we get E = -16000 N/C.

Therefore, the closest choice is A.

The Cross Section of a Long Coaxial Cable Is Shown