long nonconducting cylinder (radius = 12 cm) has a charge of uniform density (5.0 nC/m3) distributed throughout its volume. Determine the magnitude of the electric field 15 cm from the axis of the cylinder.

the magnitude of the electric field  = 27.1058 V/m

≈ 27 V/m

Explanation:

given

R(radius enclosed) = 12 cm = 0.12 m

ρ(charge density) = 5.0 nC/m³ = 5.0 × 10⁻⁹C/m³

r(radius from the axis) = 15 cm = 0.15 m

using Gauss law, which states that the electric flux through any closed surface is directly proportional to the total electric charge enclosed by this surface.

attached is the calculation of the question, using Gauss law of electrostatics

where are the vectors ?

answer; equivalent to a one(1) horsepower motor;