Line Charge+ insulating Cylindrical Shell

[hime]

Homework Statement

An infinite line of charge with linear density λ = 8.8 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.9 cm and outer radius b = 4.1 cm. The insulating shell is uniformly charged with a volume density of ρ = -659 μC/m3.

What is λ2, the linear charge density of the insulating shell?

What is Ey(P), the value of the y-component of the electric field at point P, located a distance 8.4 cm along the y-axis from the line of charge?

Homework Equations

E.dA = Q/Epsilon nought
Q=rhow*V in terms of volume charge density
Q=lambda*L in terms of linear charge density

The Attempt at a Solution

λ2 = rhow/Surface Area of the Spherical Shell
λ2 = -659 μC/m3 * 4*pi* .041^2 = -13.9 μC/m

but this is wrong! why?

 

[Doc Al]

For one thing, it's a cylindrical shell, not a spherical shell. For another, they want the linear charge density, which is the charge per unit length.

 

[hime]

well how do i go from the surface charge density to linear charge density..is there a formula for that?

 

[Doc Al]

well how do i go from the surface charge density to linear charge density..is there a formula for that?

You have a volume charge density. Find the total charge per length of that cylindrical shell. (First find the volume between the inner and outer radii.)

 

[hime]

yeah sry for those typos.
anyway, we find the volume of the shell by using formula:
=(Area of outer base-Area of inner base) * Length
=pi*(.041^2-.029^2) *Length
But i do not know the length of the cylinder, that's the main problem I am facing.

 

[Doc Al]

But i do not know the length of the cylinder, that's the main problem I am facing.

You don't need to know the length. You want the charge per unit length.

 

[hime]

oh got it! Volume charge density*Area of the shell = Linear charge density which is
-659*pi*(.041^2-.029^2)=-1.74e-6 C/m

Now, how do I find E(y) at P? Do I just use E = q/(epsilon nought * Area of the Gaussian cylinder at P) or do I use the linear charge density in the formula?

 

[Doc Al]

Whichever way you do it, you'll end up needing the linear charge density. (You'll need it to find the charge within your Gaussian surface, for example.)