Concentric Cylindrical Conducting Shells Potential Difference

In summary, the problem involves two infinitely long conducting cylindrical shells with different linear charge densities, one inside the other. The task is to find the potential difference between the two shells. This can be solved by using Gauss's law to find the electric field and then integrating over the distance from shell A to shell C.
  • #1
jeff24
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Homework Statement



An infiinitely long solid conducting cylindrical shell of radius a = 4.5 cm and negligible thickness is positioned with its symmetry axis along the z-axis as shown. The shell is charged, having a linear charge density λinner = -0.35 μC/m. Concentric with the shell is another cylindrical conducting shell of inner radius b = 17.1 cm, and outer radius c = 20.1 cm. This conducting shell has a linear charge density λ outer = 0.35μC/m.

https://www.physicsbrain.com/images/content/EM/08/h8_cylinder.png

What is V(c) – V(a), the potential difference between the the two cylindrical shells?

Homework Equations



[tex] \Delta V = V_b - V_a = \frac{{\Delta U}}{{q_0 }} = - \int_a^b {E \cdot d\ell } [/tex]

V(c)-V(a) = -integral from A to C of the Electric Field dot dl

The Attempt at a Solution



I don't know where to start. I don't even know how to get the electric field or charge of a 3-D object (outer cylindrical shell) when I'm only given lambda, charge/meter.
 
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  • #2
Use Gauss's law to get the electric field.
 

FAQ: Concentric Cylindrical Conducting Shells Potential Difference

What is a concentric cylindrical conducting shell?

A concentric cylindrical conducting shell is a type of electrical conductor that consists of two or more cylindrical layers, with each layer having a different electrical potential. The layers are arranged so that they share a common center, hence the term "concentric". These shells are commonly used in applications such as capacitors and transmission lines.

How does potential difference affect concentric cylindrical conducting shells?

Potential difference, also known as voltage, is the difference in electrical potential between two points in a circuit. In concentric cylindrical conducting shells, potential difference is the driving force behind the flow of electrical current between the layers of the shell. The larger the potential difference, the greater the flow of current between the layers.

What is the formula for calculating potential difference in concentric cylindrical conducting shells?

The formula for calculating potential difference in concentric cylindrical conducting shells is V = (Q * ln(b/a)) / (2πε0εr), where V is the potential difference, Q is the charge on the inner shell, b is the radius of the outer shell, a is the radius of the inner shell, and ε0 and εr are the permittivity of free space and relative permittivity of the material between the shells, respectively.

Why is the potential difference between concentric cylindrical conducting shells constant?

The potential difference between concentric cylindrical conducting shells is constant because the electric field between the shells is uniform. This means that the potential difference remains the same at any point between the shells, regardless of the distance from the center. This is due to the fact that the electric field lines are perpendicular to the surface of the shells, resulting in a constant potential difference.

What are some practical applications of concentric cylindrical conducting shells?

Concentric cylindrical conducting shells have a variety of practical applications in the field of electrical engineering. They are commonly used in the construction of capacitors, which are essential components in electronic circuits. They are also used in transmission lines to distribute high-voltage electricity over long distances. Additionally, they have applications in medical imaging equipment, such as MRI machines, and in the production of high-voltage equipment, such as x-ray machines.

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