# Gauss Law; Electric Field

## Homework Statement

A long non-conducting cylinder has a charge density ρ = αr, where α = 6.34 C/m4 and r is in meters. Concentric around it is a hollow metallic cylindrical shell.

Diameter 1: 4.36 cm
Diameter 2: 10.4 cm
Diameter 3: 16 cm

What is the direction of the electric field at 14.1 cm from the central axis.

3. Undetermined, since the firld is zero
4. The electric field is not a vector and therefore has no direction

## The Attempt at a Solution

Soo...since the question stated 14.1 cm from the central axis. this is outside of the cylinder. the electric field exists??? so it would be pointing radically outward?

this is incorrect!
So at this point I am unable to come up with a reason why it is not pointing radically outward?

My next assumption is that it would be pointing in the x-axis however that is not an option, and i am unsure how to relate it to the other three options. any help would be greatly appreciated.
Thank you

## The Attempt at a Solution

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SammyS
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Homework Helper
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## Homework Statement

A long non-conducting cylinder has a charge density ρ = αr, where α = 6.34 C/m4 and r is in meters. Concentric around it is a hollow metallic cylindrical shell.

Diameter 1: 4.36 cm
Diameter 2: 10.4 cm
Diameter 3: 16 cm

What is the direction of the electric field at 14.1 cm from the central axis.

3. Undetermined, since the firld is zero
4. The electric field is not a vector and therefore has no direction

## The Attempt at a Solution

Soo...since the question stated 14.1 cm from the central axis. this is outside of the cylinder. the electric field exists??? so it would be pointing radically outward?

this is incorrect!
So at this point I am unable to come up with a reason why it is not pointing radically outward?

My next assumption is that it would be pointing in the x-axis however that is not an option, and i am unsure how to relate it to the other three options. any help would be greatly appreciated.
Thank you
Look again at the location, 14.1 cm from the axis. Isn't that location within the conducting material of the cylindrical shell ?

Look again at the location, 14.1 cm from the axis. Isn't that location within the conducting material of the cylindrical shell ?

The outer diameter is 16 cm. Wouldnt that mean the radius is 8cm. So 14cm is on the outside and not on the inside...unless the question is phrased incorrectly as in, 14 cm is the diameter of and 7 is the radius. But i do not think that is the case.

SammyS
Staff Emeritus
Homework Helper
Gold Member
The outer diameter is 16 cm. Wouldnt that mean the radius is 8cm. So 14cm is on the outside and not on the inside...unless the question is phrased incorrectly as in, 14 cm is the diameter of and 7 is the radius. But i do not think that is the case.
You're right. I was thinking of those as radii, even though you clearly said they're diameters.

If the conducing shell has no net charge, the field beyond the shell points radially outward. -- You were correct.

Last edited:
You're right. I was thinking of those as radii, even though you clearly said they're diameters.

If the conducing shell has no net charge, the field beyond the shell points radially outward. -- You were correct.

Thank you for your help. You confirmed that the diagram provided is incorrect. The diameter was actually suppose to be labeled as radius…