Two infinitely long cylindrical conductors, axes

Two infinitely long cylindrical conductors, whose axes coincide, have radii R1 = 6 cm and R2 = 18 cm. The cylinders are charged uniformly and differently with a linear density of 5 * 10^-8 C/m, and the charge of the cylinder with a smaller radius is positive. The entire space between the cylindrical surfaces is filled with a homogeneous dielectric (e = 5.0).

It is necessary to construct graphs of the functions f1(r) and f2(r), where f1(r) is the potential of the electrostatic field inside a cylinder of radius R1, and f2(r) is the potential of the electrostatic field between the cylinders.

We have two infinitely long cylindrical conductors that have radii R1 = 6 cm and R2 = 18 cm. These cylinders are charged uniformly and differently with a linear density of 5 * 10^-8 C/m, while the charge of the cylinder with a smaller radius is positive. The entire space between the cylindrical surfaces is filled with a homogeneous dielectric with a relative dielectric constant e = 5.0.

To plot graphs of the functions f1(r) and f2(r), it is necessary to use the appropriate formulas. For the electrostatic field potential inside a cylinder of radius R1, the formula is:

f1(r) = (λ/(2π)) * ln(r/R1),

where λ is the linear charge density of the cylinder, ε is the absolute dielectric constant of the medium, ln is the natural logarithm, and r is the distance from the center of the cylinder to the point at which the potential is determined.

For the potential of the electrostatic field between the cylinders, the formula is:

f2(r) = (λ/(2π)) * ln(R2/R1),

where R2 is the radius of the outer cylinder.

Plotting the functions f1(r) and f2(r) can be done using plotting programs such as Python and Matplotlib.

Product description

Item name: Two infinitely long cylindrical conductors, axes

Category: Digital Products

Price: check with the seller

Description

This digital product is a unique material that is suitable for students and teachers studying electrostatics and electrodynamics.

The product includes:

• theoretical materials on the topic “Two infinitely long cylindrical conductors, axes”;
• practical tasks to consolidate the material;
• graphic materials, including graphs of functions f1(r) and f2(r);
• a list of recommended literature for a more in-depth study of the topic.

Product Features

• High-quality material compiled by experienced teachers;
• Clear presentation of the material and accessible language;
• Graphic materials in PNG format for ease of use;
• The ability to quickly and effectively study a topic at home;
• A useful tool for preparing for exams and testing.

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Product description:

This product consists of two infinitely long cylindrical conductors whose axes coincide. The first conductor has a radius R1 = 6 cm, and the second has a radius R2 = 18 cm. Both conductors are charged uniformly and differently with a linear density of 5 * 10^-8 C/m. The charge of a cylinder with a smaller radius is positive. The entire space between the cylindrical surfaces is filled with a homogeneous dielectric with a relative dielectric constant e = 5.0.

Additionally, the task was set to construct graphs of the functions f1(r) and f2(r), which will depend on the radius r. To solve the problem, it is necessary to use the laws of electrostatics, namely Coulomb's law and Gauss's theorem, as well as Poisson's equation for the electrostatic potential.

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