Electric field of a cylinderical insulator

In summary, the problem involves a long cylindrical insulator with a uniform charge density of 1.79 µC/m and a radius of 3 cm. The question asks for the electric field inside the insulator at a distance of (a) 2 cm and (b) 10 cm, with the answer for part (a) in units of N/C. To solve this problem, Gaussian Law is used by constructing a cylindrical Gaussian surface with a radius of r (where r is less than the radius of the insulator) and a length of l. The question does not provide the height, which is necessary for the solution, but the height can be cancelled out in the equation.
  • #1
peaceandlove
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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.
 
Last edited:
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  • #2
I figured out part a, but I'm still stuck on b.
 
  • #3
Figured out part b.
 

What is an electric field?

An electric field is a physical field that surrounds electrically charged particles and exerts force on other charged particles within its vicinity.

How is the electric field of a cylindrical insulator calculated?

The electric field of a cylindrical insulator can be calculated using the formula E = λ/2πε_0r, where λ is the charge per unit length, ε_0 is the permittivity of free space, and r is the distance from the center of the cylinder.

What factors affect the strength of the electric field of a cylindrical insulator?

The strength of the electric field of a cylindrical insulator is affected by the charge per unit length of the cylinder, the distance from the center of the cylinder, and the permittivity of the surrounding medium.

Can the electric field of a cylindrical insulator be uniform?

Yes, the electric field of a cylindrical insulator can be uniform if the charge per unit length is constant and the surrounding medium has a constant permittivity.

How does the electric field of a cylindrical insulator differ from that of a solid cylinder?

The electric field of a cylindrical insulator is different from that of a solid cylinder in that the electric field inside the cylindrical insulator is zero, while the electric field inside a solid cylinder is non-zero and depends on the distribution of charges within the cylinder.

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