The turns of a two-layer long solenoid are wound from

The turns of a two-layer long solenoid are wound from wire with a radius of 0.2 mm. In the first layer the current is 3 A, in the second - 1A. Determine the magnetic field strength inside the solenoid. Consider two cases: currents flow in one direction and in opposite directions.

Solution tasks 31169:

To determine the magnetic field strength inside the solenoid, we use the formula:

$$ B = \mu_0 \cdot n \cdot I $$

where $B$ is the magnetic field strength, $\mu_0 = 4\pi \cdot 10^{ -7} ~\text{H/m}$ is the magnetic constant, $n$ is the density of turns per unit length (the number of turns per unit of length), $I$ – current strength.

For a double layer solenoid:

$$ n_1 = \frac{N_1}{l}, \quad n_2 = \frac{N_2}{l} $$

where $n_1$, $n_2$ are the density of turns of the first and second layers, respectively, $N_1$, $N_2$ are the number of turns of the first and second layers, respectively, $l$ is the length of the solenoid.

For currents flowing in one direction:

$$ B = \mu_0 \cdot \left(n_1 \cdot I_1 + n_2 \cdot I_2\right) $$

Substituting the known values, we get:

$$ B = 4\pi \cdot 10^{ -7} \cdot \left(\frac{N_1}{l} \cdot 3~\text{А} + \frac{N_2}{l} \cdot 1~\text{А}\right) = 4\pi \cdot 10^{ -7} \cdot \frac{(N_1 \cdot 3 + N_2)~\text{А}}{l} $$

For currents flowing in opposite directions:

$$ B = \mu_0 \cdot \left(n_1 \cdot I_1 - n_2 \cdot I_2\right) $$

Substituting the known values, we get:

$$ B = 4\pi \cdot 10^{ -7} \cdot \left(\frac{N_1}{l} \cdot 3~\text{А} - \frac{N_2}{l} \cdot 1~\text{А}\right) = 4\pi \cdot 10^{ -7} \cdot \frac{(N_1 \cdot 3 - N_2)~\text{А}}{l} $$

Answer:

The magnetic field strength inside the solenoid with currents flowing in one direction is equal to $4\pi \cdot 10^{ -7} \cdot \frac{(N_1 \cdot 3 + N_2)~\text{A}}{l}$, with currents flowing in opposite directions, it is equal to $4\pi \cdot 10^{ -7} \cdot \frac{(N_1 \cdot 3 - N_2)~\text{A}}{l}$.

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This product is a solution to a physics problem that describes the turns of a two-layer long solenoid wound from wire with a radius of 0.2 mm and their current strength. In the first layer, the current is 3 A, in the second - 1 A. The task is to determine the magnetic field strength inside the solenoid in two cases: when the currents flow in one direction and when they flow in opposite directions. The solution to the problem is based on the application of the formula $B = \mu_0 \cdot n \cdot I$, where $B$ is the magnetic field strength, $\mu_0$ is the magnetic constant, $n$ is the density of turns per unit length, and $I$ - current strength. In solving the problem, formulas are also used to determine the density of turns and calculate the answer in each of the two cases. The solution to the problem is complete and contains all the necessary steps to successfully solve the problem. This product can be useful to students studying physics, as well as anyone who is interested in this science and wants to deepen their knowledge.

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This is a two-layer long solenoid, which consists of turns wound from wire with a radius of 0.2 mm. In the first layer the current is 3 A, and in the second layer it is 1 A.

To determine the magnetic field strength inside the solenoid, it is necessary to consider two cases: when currents flow in one direction and in opposite directions.

With currents flowing in one direction, the magnetic field strength inside the solenoid can be determined by the formula:

B = (μ0 * N * I) / L,

where B is the magnetic field strength, μ0 is the magnetic constant, N is the number of turns in the solenoid, I is the strength of the current flowing in the solenoid, L is the length of the solenoid.

For the first layer, the current is 3 A, and for the second layer - 1 A. Therefore, the total number of turns is:

N = n1 + n2,

where n1 and n2 are the number of turns in the first and second layers, respectively.

The length of the solenoid is:

L = (n1 + n2) * π * d,

where d is the diameter of the solenoid, which can be found by the formula d = 2 * r, where r is the radius of the wire.

Substituting the values ​​into the formula, we get:

B = (μ0 * (n1 + n2) * I) / ((n1 + n2) * π * d)

With currents flowing in opposite directions, the magnetic field strength inside the solenoid can be determined by the formula:

B = (μ0 * N * (I1 - I2)) / L,

where I1 and I2 are the strengths of currents flowing in the first and second layers, respectively.

Substituting the values ​​into the formula, we get:

B = (μ0 * (n1 + n2) * (I1 - I2)) / ((n1 + n2) * π * d)

The answer to the problem depends on specific values ​​that are not specified in the product description.

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