Line Charge and Charged Cylindrical Shell

In summary, a line charge differs from a point charge in that it is a one-dimensional distribution of charge along a line, while a point charge is located at a specific point. A charged cylindrical shell creates an electric field both inside and outside the shell, with zero electric field inside and a concentrated charge at the center outside. The electric potential for a line charge is calculated using V=kλ/ρ, while for a charged cylindrical shell it is calculated using V=kQ/ρ. The electric field of a line charge is given by E=kλ/2πε<sub>0</sub>ρ, and both a line charge and a charged cylindrical shell can be used to create a uniform electric field under certain conditions.
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Homework Statement



1. Homework Statement

An infinite line of charge with linear density λ = 7.5 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.9 cm and outer radius b = 4.9 cm. The insulating shell is uniformly charged with a volume density of ρ = -612 μC/m3.

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

Homework Equations





The Attempt at a Solution

 
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What are the relevant equations? How do you think you should approach this problem?
 

FAQ: Line Charge and Charged Cylindrical Shell

1. What is a line charge and how does it differ from a point charge?

A line charge refers to a one-dimensional distribution of charge along a line, while a point charge is a single charge located at a specific point. In other words, a line charge has a finite length while a point charge has no dimension.

2. How does a charged cylindrical shell behave in an electric field?

A charged cylindrical shell will create an electric field both inside and outside of the shell. Inside the shell, the electric field is zero, while outside the shell, the electric field behaves as if all the charge is concentrated at the center of the shell.

3. How is the electric potential calculated for a line charge and a charged cylindrical shell?

The electric potential for a line charge is calculated using the equation V=kλ/ρ, where k is the Coulomb constant, λ is the linear charge density, and ρ is the distance from the line charge. For a charged cylindrical shell, the electric potential is calculated using V=kQ/ρ, where Q is the total charge of the shell and ρ is the distance from the center of the shell.

4. What is the equation for the electric field of a line charge?

The electric field of a line charge is given by the equation E=kλ/2πε0ρ, where k is the Coulomb constant, λ is the linear charge density, ε0 is the permittivity of free space, and ρ is the distance from the line charge.

5. Can a line charge or a charged cylindrical shell be used to create a uniform electric field?

Yes, a line charge or a charged cylindrical shell can be used to create a uniform electric field, but only in certain conditions. For a line charge, the electric field will be uniform if the linear charge density is constant and the line charge is infinitely long. For a charged cylindrical shell, the electric field will be uniform if the charge is distributed uniformly along the shell and the shell is infinitely long.

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