Electric field of a cylinderical insulator

AI Thread Summary
The discussion focuses on calculating the electric field of a long cylindrical insulator with a uniform charge density of 1.79 µC/m and a radius of 3 cm. For part (a), the electric field inside the insulator at a distance of 2 cm is determined using Gauss’ Law. The challenge arises in part (b) when calculating the electric field at a distance of 10 cm, as the height of the Gaussian surface is not provided. The solution involves constructing a cylindrical Gaussian surface and applying the appropriate equations to find the electric field values. Ultimately, both parts of the problem are resolved using the principles of Gauss’ Law.
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Homework Statement


A long cylindrical insulator has a uniform charge density of 1.79 µC/m and a radius of 3 cm. What is the electric field inside the insultor at a distance of (a) 2 cm? [Answer in units of N/C] (b) 10 cm.

Homework Equations


∫ E • dA = Q_enclosed / e_0

The Attempt at a Solution


I know I have to use Gauss’ Law by constructing a cylindrical Gaussian surface of radius r (r<R) and length l. However, I can't seem to figure out how to get the height to cancel out since it isn't given in the question.
 
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I figured out part a, but I'm still stuck on b.
 
Figured out part b.
 

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