# Deriving Electric Field in a Charged Rod and Shell System"

• chillaxin
In summary: The distance from the rod is a variable so I'm not sure exactly how to format the equation.In summary, a long straight conducting rod with a linear charge density of +2.0uC/m is enclosed within a thin cylindrical shell with a linear charge density of -2.0uC/m. To calculate the electric field in the inner space, a Gaussian cylindrical surface can be constructed between the rod and the shell, using the equation E=q/4piEor^2. When calculating the electric field outside the shell, a Gaussian cylindrical surface can be constructed outside both the rod and the shell, resulting in a zero electric field due to the enclosed charge being zero.
chillaxin
A long straight conducting rod (or wire) carries a linear charge density of +2.0uC/m. This rod is totally enclosed within a thin cylindrical shell of radius R, which carries a linear charge density of -2.0uC/m.
A) Construct a Gaussian cylindrical surface between the rod and the shell to derive then electric field in the inner space as a function of the distance from the center of the rod.
B) Construct a Gaussian cylindrical surface outside both the rod and the shell to calculate the electric field outside the shell.

This is what i have so far.

E=q/4piEor^2
E=+2.0uC/m / 4pi8.85x10^-12(-2uC/m)^2
E=4.5x10^9Nm^2/C

Anybody?!?

chillaxin said:
A long straight conducting rod (or wire) carries a linear charge density of +2.0uC/m. This rod is totally enclosed within a thin cylindrical shell of radius R, which carries a linear charge density of -2.0uC/m.
A) Construct a Gaussian cylindrical surface between the rod and the shell to derive then electric field in the inner space as a function of the distance from the center of the rod.
B) Construct a Gaussian cylindrical surface outside both the rod and the shell to calculate the electric field outside the shell.

This is what i have so far.

E=q/4piEor^2
E=+2.0uC/m / 4pi8.85x10^-12(-2uC/m)^2
E=4.5x10^9Nm^2/C
The field is certainly not constant in the region between the rod and the cylinder. Are these anwers to multiple parts? Just the first part?

Last edited:
Unless I'm mistaken, the total charge inclosed in the whole system is zero. If the enclosed charge is zero, the electric field is zero. Thus from what I can draw, the answer to B is zero. The answer to A requires using the enclosed charge to be the positive portion and then solving for E.

## 1. How do you calculate the electric field in a charged rod and shell system?

In order to calculate the electric field in a charged rod and shell system, you will need to use the formula E = kQ/r^2, where E is the electric field, k is the Coulomb's constant, Q is the charge of the rod or shell, and r is the distance from the charge to the point where you want to calculate the electric field. You will also need to take into account the direction of the electric field, which will depend on the sign of the charge and the orientation of the rod or shell.

## 2. What is the difference between the electric field in a charged rod and a charged shell?

The main difference between the electric field in a charged rod and a charged shell is their shape. A charged rod has a long, cylindrical shape while a charged shell has a spherical shape. This difference in shape will affect the distribution of the electric field around the charged object and the way in which it interacts with other charged objects.

## 3. How do you determine the direction of the electric field in a charged rod and shell system?

The direction of the electric field in a charged rod and shell system can be determined by the direction of the force that a positive test charge would experience if placed at a certain point. The electric field will always point away from a positive charge and towards a negative charge. Additionally, the direction of the electric field will depend on the orientation of the charged rod or shell and the position of the test charge relative to the charged object.

## 4. Can the electric field in a charged rod and shell system be zero?

Yes, it is possible for the electric field in a charged rod and shell system to be zero. This can happen in certain points along the axis of a charged rod or in the center of a uniformly charged shell. In these cases, the electric fields from different parts of the rod or shell cancel each other out, resulting in a net electric field of zero at that point.

## 5. How does the distance from a charged rod or shell affect the strength of the electric field?

The strength of the electric field is inversely proportional to the square of the distance from the charged rod or shell. This means that as you move further away from the charged object, the electric field will decrease. This relationship is described by the formula E = kQ/r^2, where k is the Coulomb's constant, Q is the charge of the rod or shell, and r is the distance from the charge to the point where you want to calculate the electric field.

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