Circular conductor with a radius of 5.2 cm with a current I1 = 13.4 A and

In the same plane there is a circular conductor with a radius of 5.2 cm with a current I1 = 13.4 A and a straight conductor with a current I2 = 22 A. The distance from the straight conductor to the center of the circular current is 8.3 cm. It is necessary to find the magnetic field induction in the center circular current if the conductors are in the air. It is also necessary to determine the induction at the same point if the direction of the current in a straight conductor changes to the opposite.

To solve the problem, we use the formula for calculating the magnetic field from a current-carrying conductor:

B = (μ0 * I)/(2 * π * r)

where B is the magnetic field induction, μ0 is the magnetic constant (4π * 10^-7 Wb/(A * m)), I is the current strength, r is the distance from the conductor to the point at which the field induction is determined.

To find the magnetic field induction at the center of the circular current, it is necessary to substitute the values ​​in the formula:

B1 = (4π * 10^-7 * 13.4)/(2 * π * 0.052) ≈ 0.00438 Тл

Answer: the magnetic field induction at the center of the circular current under these conditions is equal to 0.00438 Tesla.

To find the magnetic field induction at the same point when the direction of the current in a straight conductor changes to the opposite, it is necessary to replace the value of the current strength with the opposite one and substitute it into the formula:

B2 = (4π * 10^-7 * (-22))/(2 * π * 0.083) ≈ -0.00140 Тл

Answer: the magnetic field induction at the same point when the direction of the current in a straight conductor changes to the opposite is equal to -0.00140 T (a negative value indicates that the direction of the magnetic field induction in this case is opposite to the direction of the magnetic field induction in the first case).

Circular conductor with current I1=13.4 A

Our digital product is a description of a problem in which a circular conductor with a radius of 5.2 cm with a current I1 = 13.4 A is considered. This problem can be useful for both students and teachers studying electromagnetism.

• Circular conductor radius: 5.2cm
• Circular conductor current: 13.4 A

Our product contains a detailed solution to the problem, formulas and laws used in the solution, derivation of the calculation formula and the answer. We also provide the opportunity to ask questions about the solution, which we will be happy to answer.

Our digital product is a description of a problem in which a circular conductor with a radius of 5.2 cm with a current I1 = 13.4 A and a straight conductor with a current I2 = 22 A are considered. It is necessary to find the magnetic field induction at the center of the circular current if the conductors are in air. It is also necessary to determine the induction at the same point if the direction of the current in a straight conductor changes to the opposite.

To solve the problem, a formula is used to calculate the magnetic field from a current-carrying conductor: B = (μ0 * I)/(2 * π * r) where B is the magnetic field induction, μ0 is the magnetic constant (4π * 10^-7 Wb/(A * m)), I is the current strength, r is the distance from the conductor to the point at which the field induction is determined.

To find the magnetic field induction at the center of the circular current, it is necessary to substitute the values ​​in the formula: B1 = (4π * 10^-7 * 13.4)/(2 * π * 0.052) ≈ 0.00438 T Answer: the magnetic field induction at the center of the circular current under these conditions is equal to 0.00438 Tesla.

To find the magnetic field induction at the same point when the direction of the current in a straight conductor changes to the opposite, it is necessary to replace the value of the current strength with the opposite one and substitute it into the formula: B2 = (4π * 10^-7 * (-22))/(2 * π * 0.083) ≈ -0.00140 T Answer: the magnetic field induction at the same point when the direction of the current in a straight conductor changes to the opposite is equal to -0.00140 T (a negative value indicates that the direction of the magnetic field induction in this case is opposite to the direction of the magnetic field induction in the first case).

Our product contains a detailed solution to the problem, formulas and laws used in the solution, derivation of the calculation formula and the answer. We also provide the opportunity to ask questions about the solution, which we will be happy to answer.

Our product is a detailed solution to the problem in which you need to find the magnetic field induction in the center of a circular conductor with a radius of 5.2 cm with a current I1 = 13.4 A and a straight conductor with a current I2 = 22 A, located at a distance of 8.3 cm from center of the circular conductor. Both conductors are in the air.

To solve the problem, we use the formula for calculating the magnetic field from a conductor with current: B = (μ0 * I)/(2 * π * r), where B is the magnetic field induction, μ0 is the magnetic constant (4π * 10^-7 Wb /(A * m)), I - current strength, r - distance from the conductor to the point at which the field induction is determined.

To find the magnetic field induction at the center of a circular conductor, we substitute the values ​​into the formula: B1 = (4π * 10^-7 * 13.4)/(2 * π * 0.052) ≈ 0.00438 T. Answer: the magnetic field induction at the center of the circular current under these conditions is equal to 0.00438 Tesla.

To find the magnetic field induction at the same point when the direction of the current in a straight conductor changes to the opposite, we replace the value of the current strength with the opposite one and substitute it into the formula: B2 = (4π * 10^-7 * (-22))/(2 * π * 0.083) ≈ -0.00140 T. Answer: the magnetic field induction at the same point when the direction of the current in a straight conductor changes to the opposite is equal to -0.00140 T (a negative value indicates that the direction of the magnetic field induction in this case is opposite to the direction of the magnetic field induction in the first case).

Our product contains a detailed solution to the problem, formulas and laws used in the solution, derivation of the calculation formula and the answer. We also provide the opportunity to ask questions about the solution, which we will be happy to answer.

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a circular conductor with a radius of 5.2 cm with a current I1 = 13.4 A is in the same plane as a straight conductor with a current I2 = 22 A. The distance from the straight conductor to the center of the circular conductor is 8.3 cm.

To solve the problem, it is necessary to find the magnetic field induction in the center of a circular conductor. To do this, you can use the Biot-Savart-Laplace law, which states that the magnetic field at point P created by a current element is proportional to the magnitude of the current and the length of the element, and also inversely proportional to the square of the distance from the element to point P:

dB = (μ₀/4π) * I * dl x r / r^3

where dB is the element of the magnetic field, I is the current, dl is the element of the length of the conductor, r is the distance from the element to point P, μ₀ is the magnetic constant.

For a circular conductor, the element of length can be represented as a circular arc, and for a straight conductor - as a segment.

The magnetic field induction at the center of a circular conductor is equal to the sum of the magnetic field elements of all conductor elements:

B = ∑dB = (μ₀/4π) * I1 * ∫dl x r / r^3

where ∫dl is the integral along the circumference of a circular conductor.

For a straight conductor, the magnetic field induction at the center of a circular conductor is equal to:

B' = (μ₀/4π) * I2 * l / r^2

where l is the length of a straight conductor.

If you change the direction of the current in a straight conductor to the opposite, then the magnetic field induction in the center of the circular conductor will also change to the opposite value.

Solution tasks:

First you need to find the magnetic field element for a circular conductor:

dB = (μ₀/4π) * I1 * dl x r / r^3

dl = r * dφ, where dφ is the differential of the angle traversed by the conductor.

Thus, dB = (μ₀/4π) * I1 * r * dφ * sin(φ) / R^2, where R is the radius of the circle on which the conductor arc element is located.

Integrating over the entire circle, we get:

B = ∑dB = (μ₀/4π) * I1 * ∫dl x r / r^3 = (μ₀/4π) * I1 * ∫0^2π r * dφ * sin(φ) / R^2 = (μ₀/4π ) * I1 * 2π * r / R^2

Substituting the values, we get:

B = (4p10^-7 * 13,4 * 2 * 5,2)/(8,310^-2) ≈ 0.021 Tl

For a straight conductor:

B' = (μ₀/4π) * I2 * l / r^2 = (4π10^-7 * 22 * 8,310^-2)/(5.2*10^-2)^2 ≈ 0.10 Tl

Answer:

The magnetic field induction at the center of a circular conductor is 0.021 Tesla. When the direction of current in a straight conductor is reversed, the magnetic field induction in the center of the circular conductor will change to the opposite value. The magnetic field induction in the center of the circular conductor will be equal to -0.10 Tesla.

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