Two conductors in the form of half rings lie in the same plane

Two conductors in the shape of half rings are located in the same plane with a common center. It is necessary to determine the voltage in the center of the semi-rings with the following data: the radius of the first semi-ring is 10 cm, the radius of the second is 20 cm, the direction of the current is the same, and the current strength is respectively 1 A and 4 A. The field created by the conducting conductors is not taken into account.

To solve this problem, we will use the Biot-Savart-Laplace law, which allows us to calculate the magnetic induction at a distance r from a straight wire through which current I flows:

B = (μ₀ / 4π) * I * dl x r / r³

where μ₀ is the magnetic constant, dl is the length of the wire element through which the current flows, r is the distance from the wire element to the point where magnetic induction is calculated.

The magnetic field strength in the center of the semirings is calculated by the formula:

B = (μ₀ / 4π) * I * (2R) / R³

where I is the current strength, R is the radius of the semiring.

For the first semi-ring, the radius R₁ = 0.1 m, the current strength I₁ = 1 A. Then the magnetic field strength at the center of the first semi-ring will be equal to:

B₁ = (μ₀ / 4π) * 1 A * (2 * 0.1 m) / (0.1 m)³ = 2 * 10⁻⁵ T

For the second semi-ring, the radius is R₂ = 0.2 m, the current strength is I₂ = 4 A. Then the magnetic field strength in the center of the second semi-ring will be equal to:

B₂ = (μ₀ / 4π) * 4 A * (2 * 0.2 m) / (0.2 m)³ = 1.6 * 10⁻⁴ T

Thus, the magnetic field strength in the center of the semirings will be equal to the sum of the magnetic field strengths created by each semiring:

B = B₁ + B₂ = 1,8 * 10⁻⁴ Тл

Answer: the magnetic field strength in the center of the semirings is 1.8 * 10⁻⁴ T.

Product description

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This task will help pupils and students more deeply understand the principles of operation of electrical circuits, as well as the Biot-Savart-Laplace law.

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Product description: this digital product is a problem from the field of electromagnetism and physics, in which it is necessary to determine the magnetic field strength in the center of two conductors in the form of semirings with a common center. The radius of the first semi-ring is 10 cm, the second - 20 cm, and the current strength in the first and second semi-ring is respectively 1 A and 4 A. The digital product includes a detailed solution to the problem with a brief recording of the conditions, formulas and laws used in the solution, conclusion calculation formula and answer. All materials are presented in a convenient format, which allows you to quickly and easily master this material. By choosing this digital product, you get a unique opportunity to improve your knowledge in the field of electromagnetism and physics, as well as cope more successfully with exams and tests.

Product description:

This digital product is a detailed solution to a problem from the field of electromagnetism and physics, described in the condition “Two conductors in the form of half rings lie in the same plane.” The task will help pupils and students more deeply understand the principles of operation of electrical circuits, as well as the Bio-Savart-Laplace law.

The digital product includes a detailed description of the problem conditions, formulas, laws and methods used in the solution, the derivation of the calculation formula and the answer. All materials are presented in a convenient format, which allows you to quickly and easily master this material.

Beautiful design in HTML format allows you to comfortably read and study the material, as well as easily return to the desired part of the task. By choosing this digital product, you get a unique opportunity to improve your knowledge in the field of electromagnetism and physics, as well as cope more successfully with exams and tests. If you have any questions about solving a problem, you can contact the author of the product for help.

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The task is to determine the tension in the center of two semirings that have a common center and some characteristics.

Task conditions:

Two conductors in the form of half rings lie in the same plane and have a common center. Determine the voltage in the center of the semirings given the following data: the radius of the first semiring is 10 cm, the second is 20 cm, the currents flow in one direction and the current strength is respectively 1 and 4 A. The field from the conducting conductors is not taken into account. Problem 31179.

Answer:

To solve the problem, we use the formula to calculate the magnetic field strength at the center of the semiring:

B = (μ0 * I) / (2 * R)

where B is the magnetic field strength, μ0 is the magnetic constant, I is the current strength, R is the radius of the semiring.

For the first semiring:

B1 = (4π * 10^-7 * 1) / (2 * 0.1) = 6.28 * 10^-6 T

For the second half ring:

B2 = (4π * 10^-7 * 4) / (2 * 0.2) = 1.26 * 10^-5 T

Answer: The magnetic field strength in the center of the first semiring is 6.28 * 10^-6 T, and in the center of the second semiring - 1.26 * 10^-5 T.

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