The figure shows a section of a long coaxial section

The figure shows a cross-section of a section of a long coaxial cable. The radii of its metal cores are equal to R1=3 mm, R2=4 mm, r=2 mm, and the currents in them are equal to I1=15 A, I2=10 A. Considering that the currents flow in one direction, it is necessary to plot the dependence of the magnetic induction fields from the distance to the cable axis B=B(r) to scale. It is also necessary to determine the magnetic field energy stored between the metal conductors of the cable per unit length. To solve the problem, we will use the formula for calculating the magnetic field induction from the current flowing through the conductor: B = (μ0/4π) * (2I/r), where μ0 is the magnetic constant equal to 4π * 10^(-7) H/m; I – current flowing through the conductor; r is the distance from the conductor to the point at which the magnetic field induction is calculated. To calculate the magnetic field induction at points located between the conductors, it is necessary to use the superposition principle: B = B1 + B2, where B1 and B2 are the magnetic field inductions created by the corresponding conductors. Let's plot the dependence of the magnetic field induction on the distance to the cable axis B=B(r) on a scale: To calculate the magnetic field energy stored between the metal conductors of the cable per unit length, we use the formula: W = (μ0/4π) * ∫ (B^2)/2 dV, where V is the volume between the metal conductors of the cable. Integrating over the volume, we obtain: W = (μ0/8π) * ((I1 * I2)/(R2 - R1)), where R1 and R2 are the radii of the metal conductors of the cable, I1 and I2 are the currents in the conductors. Thus, the magnetic field energy stored between the metal conductors of the cable per unit of its length is equal to (μ0/8π) * ((15 * 10)/(4 - 3)) = 5.3 * 10^(-6) J/m. Problem 30749. Detailed solution with a brief record of the conditions, formulas and laws used in the solution, derivation of the calculation formula and answer. If you have any questions regarding the solution, please write. I try to help. Our digital product is a unique product that will help you solve electrodynamics problems easily and quickly. The picture you can see below shows a section of a long coaxial cable. Our product contains a detailed solution to the problem for a given section of cable with a brief record of the conditions, formulas and laws used in the solution, the derivation of the calculation formula and the answer. By purchasing our digital product, you will gain access to simple, clear information that will help you easily understand complex electrodynamics problems.

Our digital product is a detailed solution to the problem of a section of a long coaxial cable, which is shown in the figure. Given are the radii of the metal conductors of the cable R1=3 mm, R2=4 mm, the distance to the cable axis r=2 mm, and the currents in the conductors I1=15 A, I2=10 A, which flow in one direction.

To plot the dependence of the magnetic field induction on the distance to the cable axis B=B(r) on a scale, we will use the formula for calculating the magnetic field induction on the current flowing through the conductor: B=(μ0/4π) * (2I/r), where μ0 is a magnetic constant equal to 4π * 10^(-7) H/m, I is the current flowing through the conductor, r is the distance from the conductor to the point at which the magnetic field induction is calculated.

To calculate the magnetic field induction at points located between the conductors, it is necessary to use the superposition principle: B=B1+B2, where B1 and B2 are the magnetic field inductions created by the corresponding conductors.

Let's plot the dependence of the magnetic field induction on the distance to the cable axis B=B(r) on a scale:

To calculate the magnetic field energy stored between the metal conductors of the cable per unit of its length, we use the formula: W=(μ0/4π) * ∫(B^2)/2 dV, where V is the volume between the metal conductors of the cable.

Integrating over the volume, we obtain: W=(μ0/8π) * ((I1 * I2)/(R2 - R1)), where R1 and R2 are the radii of the metal conductors of the cable, I1 and I2 are the currents in the conductors.

Thus, the magnetic field energy stored between the metal conductors of the cable per unit of its length is equal to (μ0/8π) * ((15 * 10)/(4 - 3)) = 5.3 * 10^(-6) J/m.

Our digital product is a complete solution to a given problem with a brief record of the conditions, formulas and laws used in the solution, the output of the calculation formula and the answer. By purchasing our product, you will have access to simple and understandable information that will help you easily understand similar problems in electrodynamics. If you have any questions about the solution, you can always contact us and we will try to help you.

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This product is a problem from the field of electromagnetism, which describes a coaxial cable with metal conductors. The figure shows a section of a section of a long coaxial cable, where the radii of its metal cores are equal to R1=3 mm, R2=4 mm, and the radius of the middle shell is r=2 mm. The currents in the metal conductors are equal to I1=15 A, I2=10 A and flow in one direction.

It is necessary to construct a scale graph of the dependence of the magnetic field induction on the distance to the cable axis B=B(r) and determine the magnetic field energy stored between the metal conductors of the cable per unit length.

To solve the problem, the laws of electromagnetism are used, namely the Biot-Savart-Laplace law, which allows one to calculate the magnetic field induction B at a point located at a distance r from the cable axis, and formulas for calculating the magnetic field energy.

After calculating the magnetic field induction at point r and the magnetic field energy stored between the metal conductors of the cable per unit length, it is necessary to derive the calculation formula and answer to the problem.

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