# Line Charge and Charged Cylindrical Shell (Gauss law)

## 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?

## 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.

Last edited:

haruspex
Homework Helper
Gold Member
2020 Award
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.

BruceW
Homework Helper
ah! you beat me to it haruspex

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