# Line Charge+ insulating Cylindrical Shell

## 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?

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Doc Al
Mentor
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.

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

Doc Al
Mentor
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.)

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, thats the main problem im facing.

Doc Al
Mentor
But i do not know the length of the cylinder, thats the main problem im facing.
You don't need to know the length. You want the charge per unit length.

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
Mentor
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.)