A long nonconducting cylinder (radius = 6.0 mm) has a nonuniform volume charge density given by αr², where α = 6.2 mC/m⁵ and r is the distance from the axis of the cylinder. What is the magnitude of the electric field at a point 2.0 mm from the axis? A) 1.4 N/C B) 1.6 N/C C) 1.8 N/C D) 2.0 N/C E) 5.4 N/C

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Quizplus · Accepted Answer

The electric field inside a nonconducting cylinder with a nonuniform charge density can be found using Gauss's law. The charge density is given by αr², so the charge enclosed by a Gaussian surface at radius r is integrated over the volume. For r = 2.0 mm, the electric field is calculated using the formula E = (αr³)/(3ε₀), where ε₀ is the permittivity of free space. Substituting the given values, the electric field is approximately 1.4 N/C.

A Long Nonconducting Cylinder (Radius = 6