In the middle part of the long solenoid there is a segment

In the middle part of the long solenoid there is a piece of conductor 2 cm long, through which a current of 4 A flows. The conductor is located perpendicular to the axis of the solenoid. A force of 10^-5 N acts on this section of conductor. It is necessary to find the current strength in the solenoid winding, provided that there are 10 turns for every centimeter of solenoid length and there is no core.

To solve the problem, we will use the Biot-Savart-Laplace law, which describes the magnetic field created by a current in a conductor. According to this law, the magnetic field created on a piece of conductor is proportional to the current strength in the conductor, the length of the conductor and the number of turns per unit length of the solenoid. Thus, the following equation can be written:

B = (mu * N * I) / L,

where B is the magnetic induction, mu is the magnetic constant, N is the number of turns per unit length, L is the length of the conductor, and I is the current strength in the conductor.

It is known that a force caused by the interaction of a magnetic field with the current strength acts on a piece of conductor. This force is equal to:

F = B * I * L.

By substituting the value of the current and the length of the conductor, we can express the magnetic induction:

B = F / (I * L) = 10^-5 N / (4 A * 0.02 m) = 1.25 Tl.

Thus, the magnetic induction on a piece of conductor is 1.25 Tesla. It is known that for every centimeter of solenoid length there are 10 turns, and there is no core. Therefore, the number of turns in the solenoid winding is equal to:

N = (solenoid length) * (number of turns per unit length) = 100 cm * 10 = 1000.

Finally, the current in the solenoid winding is calculated by the formula:

I' = B * L * N / mu = (1.25 T) * (100 cm) * (1000) / (4 * pi * 10^-7 T * m / A) = 9.92 A.

Thus, the current in the solenoid winding is 9.92 A.

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This product is a physics problem that describes the calculation of the current strength in the solenoid winding.

The condition states that in the middle part of the long solenoid there is a piece of conductor 2 cm long and with a current of 4 A, located perpendicular to the axis of the solenoid, which is acted upon by a force of 10^-5 N. It is also known that there are 10 turns per 1 cm of solenoid length and the core is missing.

To solve the problem, it is necessary to use the Biot-Savart-Laplace law, which allows one to calculate the magnetic field at any point in space around the current. Formula for calculating the magnetic field on the solenoid axis: B = μ₀ * N * I / L, where B is the magnetic induction, μ₀ is the magnetic constant, N is the number of turns per 1 meter of solenoid length, I is the current strength in the solenoid winding, L - solenoid length.

To find the magnetic induction on the solenoid axis, it is necessary to know the number of turns per 1 cm of solenoid length: N = 10. Then the magnetic induction on the solenoid axis will be equal to: B = μ₀ * 10 * I / 1.

The force acting on a piece of conductor is equal to the product of the current and the length of the conductor by the magnetic induction on the axis of the solenoid: F = I * l * B. Substituting the known values, we get: F = 4 * 0.02 * μ₀ * 10 * I.

Since F = 10^-5 N, we can express I: I = F / (4 * 0.02 * μ₀ * 10). Substituting numerical values, we get: I ≈ 1.26 A.

Answer: The current in the solenoid winding under given conditions is approximately 1.26 A.

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