Electric Fields of Cylinders and Cylindrical Shells

[tristanm]

Homework Statement

1. Use Gauss' Law to calculate the electric field at a radius of 5.0cm from the z-axis
2. Use Gauss' Law to calculate the electric field at a radius of 8.0cm from the z-axis
3. What is the surface charge density σ_metal on the outer surface of the metal cylinder?

Homework Equations

∫EdA = [itex]\frac{Q_Enclosed}{ε_o}[/itex]
σ=Q*A
A=2πrL
ρ=[itex]\frac{Q_insulator}{ε_o(c²-b²)L}[/itex]

The Attempt at a Solution

1. Using Gauss' law, I took E and A out of the integral as they are both in the same direction, moved A over to the RHS of the equation, and subbed in 2πrL to give [itex]\frac{Q_enclosed}{ε_o2πrL}[/itex]
I then put in the values in meters, μCs and got -7.1901E⁴N/C

2. E of the insulator is equal to [itex]\frac{Q_enclosed}{ε_o}[/itex] which is equal to [itex]\frac{ρπ(r²-b²)L}{2ε_or}[/itex]
which gives the result of 4.0724E⁴N/C
Adding this value to E_metal I get -3.1176E⁴N/C

I'm not sure whether or not this is the correct procedure to calculate the electric field inside the shell's material, however for part 1. I know that inside the shell it has no electric field.

3. Is this just a matter of using σ=Q*A where Q is the charge of the metal and A is (2πr² + 2πrl)?
I did this and got -2.7527E^-5


Aside: Why are my [/itex] formatting not working?

 

[haruspex]

Why are my [/itex] formatting not working?

Because you put non-LaTeX controls (sub, /sub) inside. Use _{} etc.:
$\frac{Q_{Enclosed}}{ε_o}$

 

[tristanm]

Because you put non-LaTeX controls (sub, /sub) inside. Use _{} etc.:
$\frac{Q_{Enclosed}}{ε_o}$

That makes sense. I can't seem to edit my post for some reason, but no matter.

What about the actual physics question?

 

[haruspex]

That makes sense. I can't seem to edit my post for some reason, but no matter.

What about the actual physics question?

Sorry for the delay - sporadic internet access.
For 1, the formula looks ok - haven't checked the numbers.
For 2, you seem to be missing some terms in the denominator (like those in your equation for 1). You've also missed out some algebraic steps in getting to the numerical result. If you post all your algebra I'm happy to check that.

 

[tristanm]

Sorry about replying so late. I did in fact figure it out! Thank you for the help