# Electric field at a point from an insulating shell

#### rezal

1. Homework Statement
An infinite line of charge with linear density λ1 = 6.9μ C/m is positioned along the axis of a thick insulating shell of inner radius a = 2.6 cm and outer radius b = 4.8 cm. The insulating shell is uniformly charged with a volume density of ρ = -656μ C/m3

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

2)What is Ey(P), the value of the y-component of the electric field at point P, located a distance 8.3 cm along the y-axis from the line of charge?
2. Homework Equations
$$1) E=\frac{1}{4\pi\epsilon_0} \frac{q_0}{r^2}$$
$$2) \int E \bullet dA = \frac{Q}{\epsilon_0}$$

3. The Attempt at a Solution
For 1, I found λ2 with $$\rho\pi(b^2 - a^2)$$ and it turned out to be λ2 = -3.36E-6 C/m

I'm stuck on 2, I tried doing it by adding three electric fields. The first one in the shells' center using λ1 with equation 1, the second one in the shell using the charge from ρV with equation 2, and the third one in a cylindrical gaussian surface that has P on its surface with equation 2. I keep getting 1.8E8 C/m which is wrong.

Can someone tell me where i'm going wrong with this?

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#### ehild

Homework Helper
1. Homework Statement
An infinite line of charge with linear density λ1 = 6.9μ C/m is positioned along the axis of a thick insulating shell of inner radius a = 2.6 cm and outer radius b = 4.8 cm. The insulating shell is uniformly charged with a volume density of ρ = -656μ C/m3

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

2)What is Ey(P), the value of the y-component of the electric field at point P, located a distance 8.3 cm along the y-axis from the line of charge?
2. Homework Equations
$$1) E=\frac{1}{4\pi\epsilon_0} \frac{q_0}{r^2}$$
$$2) \int E \bullet dA = \frac{Q}{\epsilon_0}$$

3. The Attempt at a Solution
For 1, I found λ2 with $$\rho\pi(b^2 - a^2)$$ and it turned out to be λ2 = -3.36E-6 C/m

I'm stuck on 2, I tried doing it by adding three electric fields. The first one in the shells' center using λ1 with equation 1, the second one in the shell using the charge from ρV with equation 2, and the third one in a cylindrical gaussian surface that has P on its surface with equation 2. I keep getting 1.8E8 C/m which is wrong.

Can someone tell me where i'm going wrong with this?
Equation 1 can not be used, as it refers to a point charge. Apply Gauss' Law (eq. 2 ) and remember, Q is the charge enclosed by the Gaussian surface.

#### rezal

Equation 1 can not be used, as it refers to a point charge. Apply Gauss' Law (eq. 2 ) and remember, Q is the charge enclosed by the Gaussian surface.
Ah alright, I got it now. Thank you!

"Electric field at a point from an insulating shell"

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