# Conductor with shell problem getting zero as answer?

• AGGENGR
In summary, the conversation revolved around a cylindrical cable with an outer tube made of copper and an inner copper wire with charge densities of -2λ and +λ respectively. The problem at hand was to determine the surface charge density at the outer surface of the tube, which was found to be zero using the formula sigma=q/A. The work done to reach this solution is shown in the attached image. A correction was made to the formula and the resulting value for the surface charge density now makes sense.
AGGENGR
1. Problem Statement:

The figure shows a cross-section view of a very long cylindrical cable. There is an outer tube
concentric with the tube. The inner wire has charge density –2λ (per unit length), while the tube
carries total charge +λ. [You need to show solution method to get full credit on this problem!]
(a) How does the charge arrange itself on the outer tube? On outside of course!
b) What is the surface charge density (σ) at the outer surface of the tube, at 4R? Getting zero for this one?

2. Homework Equations
sigma=q/A

3. Work.
So I used the above formula and got zero for some odd reason. I calculated the sigma inner and that's what giving me zero. Work is attached in jpeg.

#### Attachments

• 20140927_154940.jpg
30.1 KB · Views: 390
Hi. Check... $\frac{\lambda - 4\lambda \pi R}{8 \pi R} \neq \frac{\lambda-\lambda}{2}$.

AGGENGR
Ahhh makes sense now. Thanks!

## 1. What is the "conductor with shell problem"?

The conductor with shell problem, also known as the "concentric spherical shells problem", is a theoretical physics problem that involves finding the electric field inside and outside of a series of concentric spherical shells with different charges.

## 2. Why is the answer to the conductor with shell problem often zero?

The answer to the conductor with shell problem is often zero because the electric field inside a conductor is always zero. This is due to the fact that charges inside a conductor will redistribute themselves until they are in a state of electrostatic equilibrium, resulting in a cancellation of the electric field inside the conductor.

## 3. Is the conductor with shell problem a real-world scenario?

The conductor with shell problem is a theoretical scenario often used in physics education to demonstrate the principles of electrostatics. While it may not occur exactly as described in real-world situations, it helps to understand the behavior of electric fields and charges in a simplified setting.

## 4. How do you solve the conductor with shell problem?

To solve the conductor with shell problem, you can use the principle of superposition, which states that the total electric field at a point is the vector sum of the individual electric fields from each charge. By applying this principle to each shell, you can find the electric field at any point both inside and outside of the shells.

## 5. What is the significance of the conductor with shell problem?

The conductor with shell problem is significant in understanding the behavior of electric fields and charges in a simplified setting. It also helps to illustrate the concept of electrostatic equilibrium and the principle of superposition, which are important principles in the study of electromagnetism and other related fields of science.

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