Question

Катушка с диаметром 0,5 м содержится в сменном магнитном поле. При изменении индукции на 130 Тл за 2 с в обмотке катушки возбуждаются ЭДС самоиндукции 25 В. Сколько витков имеет катушка?

Answer 1

Ответ:

Катушка состоит из 2 витков

Объяснение:

Дано:

D = 0,5 м

ΔB = 130 Тл

Δt = 2 с

$\xi =$ 25 В

Найти:

N - ?

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Решение:

$\boxed{\xi = N \bigg |\dfrac{з \Phi}{зt} \bigg|}$ - самоиндукция катушки состоящей из N витков

$\boxed{з \Phi = з B \cdot S}$ - так как в данной задаче магнитная индукция сонаправленна с нормалью к плоскости, то угол между сонаправленными векторами равен 0°, а cos 0° = 1, поэтому косинус угла можно не записывать в данном случае.

$\xi = N\cdot \dfrac{ з B \cdot S}{зt} \Longrightarrow \boxed{ N = \dfrac{зt \cdot \xi}{з B \cdot S} = \dfrac{зt \cdot \xi}{з B \cdot 0,25 \pi D^{2}} }$

N = (2 с * 25 В) / (130 Тл * 0,25 * 3,14 * 0,25 м²) = 2 витка

Ответ: N = 2. Катушка состоит из 2 витков.

Answer 2

Calculation of the number of turns in the coil

To calculate the number of turns in the coil, we can use the formula for self-inductance:

L = (N * Φ) / I

Where: - L is the self-inductance of the coil, - N is the number of turns in the coil, - Φ is the magnetic flux through the coil, and - I is the current flowing through the coil.

In this case, we are given the following information: - The diameter of the coil is 0.5 m. - The change in magnetic induction is 130 T. - The time taken for the change is 2 s. - The induced electromotive force (EMF) due to self-induction is 25 V.

We need to find the number of turns in the coil (N).

To calculate the magnetic flux (Φ), we can use the formula:

Φ = B * A

Where: - B is the magnetic field strength, and - A is the area of the coil.

The area of the coil can be calculated using the formula for the area of a circle:

A = π * r^2

Where: - r is the radius of the coil.

Given that the diameter of the coil is 0.5 m, the radius (r) is 0.25 m.

Now, let's calculate the area of the coil:

A = π * (0.25)^2

A = 0.19634954084936207 m^2

Next, we can calculate the magnetic flux (Φ) using the given change in magnetic induction (130 T) and the area of the coil (0.19634954084936207 m^2):

Φ = 130 T * 0.19634954084936207 m^2

Φ = 25.52043552381547 Wb

Now, we can rearrange the formula for self-inductance to solve for the number of turns (N):

N = (L * I) / Φ

Given that the induced EMF due to self-induction is 25 V, we can substitute this value into the formula:

N = (25 V * I) / Φ

To find the value of I, we can use Ohm's law:

I = V / R

Where: - V is the induced EMF, and - R is the resistance of the coil.

Unfortunately, the resistance of the coil is not provided in the question. Without this information, we cannot calculate the current flowing through the coil (I) and, consequently, the number of turns in the coil (N).

Please provide the resistance of the coil so that we can proceed with the calculation.