Line Charge and Charged Cylindrical Shell (Gauss law)

[Sneakatone]

Homework Statement

An infinite line of charge with linear density λ1 = 6.2 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.7 cm and outer radius b = 4.4 cm. The insulating shell is uniformly charged with a volume density of ρ = -552 μC/m3.1) What is λ2, the linear charge density of the insulating shell?
-2.093 μC/m
2) What is Ex(P), the value of the x-component of the electric field at point P, located a distance 7.5 cm along the y-axis from the line of charge?
0 N/C

3) What is Ey(P), the value of the y-component of the electric field at point P, located a distance 7.5 cm along the y-axis from the line of charge?

Homework Equations

The Attempt at a Solution

number 3 is the one I am stuck on. I used gauss law and ended with the equation E(x)=landa/(2pi (8.85*10^-12 * r) and got 503541.06 N/C but it seems to be wrong.

 

[haruspex]

number 3 is the one I am stuck on. I used gauss law and ended with the equation E(x)=landa/(2pi (8.85*1-^-12 * r) and got 503541.06 N/C but it seems to be wrong.

I get nearly double that. Please post your working.

 

[BruceW]

ah! you beat me to it haruspex

 

[Sneakatone]

I used gauss law
integral(E*dA)=q_in/epsilon
LHS E∫dA RHS ∫(from 0 to h) (λ1*dz)/(ε0)
2pi*dx*h*E= (λ1*h)/ε0
E=λ/(2*∏*ε0*dR)

 

[haruspex]

Yes, those are the equations, but I asked to see the working. can't tell where you're going wrong without that. you are adding the fields for the two charges, right?