Net charge inside a cylinder

[Fatima Hasan]

Homework Statement

Homework Equations

The Attempt at a Solution

Here's my work :

 

[TSny]

Your expressions for the areas don't look correct. When calculating $\Phi_0$, what particular area are you working with? What is the formula for this particular area ?

 

[Fatima Hasan]

Your expressions for the areas don't look correct. When calculating $\Phi_0$, what particular area are you working with? What is the formula for this particular area ?

 

[TSny]

Which parts of the surface of the cylinder have nonzero flux?

 

[Fatima Hasan]

Which parts of the surface of the cylinder have nonzero flux?

The area that we're concerned will be the surface area of the ends of Gaussian surface which is equals to π / R^2
Φ = E A = Q enclosed / ε
Q enclosed = $100 * π * (0.1)^2 * 8.85 = 27.8 pC$

 

[TSny]

The area that we're concerned will be the surface area of the ends of Gaussian surface which is equals to π / R^2

Of course you mean π⋅R^2.

Φ = E A = Q enclosed / ε
Q enclosed = 100 * π * (0.1)^2 * 8.85 = 27.8 pC

This is correct.

 

[Fatima Hasan]

Of course you mean π⋅R^2.
This is correct.

$A = 2 \pi r h$ , we use this formula to find the net flux through a cylinder , right ?

 

[TSny]

$A = 2 \pi r h$ , we use this formula to find the net flux through a cylinder , right ?

Not in this problem. The area $A = 2 \pi r h$ is the "lateral" area of the curved surface of the cylinder, as shown below in blue

Is there any flux through the blue surface in the problem you are working on?

 

[Fatima Hasan]

Not in this problem. The area $A = 2 \pi r h$ is the "lateral" area of the curved surface of the cylinder, as shown below in blue
View attachment 221399

Is there any flux through the blue surface in the problem you are working on?

No