Question

Колебательный контур, состоящий из катушки и плоского конденсатора, настроен на электромагнитную волну с частотой = 0, 05 МГц. Определи индуктивность катушки L, если пространство между обкладками площади S = 50 см" заполнено диэлектриком с диэлектрической проницаемостью E = 10, а расстояние между обкладками равно d = 1 мм. Ответ вырази в мГн, округлив результат до целого значения.

Answer 1

Ответ:

я знаю только формулу, но сопоставить не могу

Однако наиболее простая формула, которая позволяет вычислить многие неизвестные величины, - формула Томсона (названа в честь английского физика Уильяма Томсона, который вывел её в 1853 году): T = 2*п*(L*C)1/2.T - период электромагнитных колебаний, L и C - соответственно, индуктивность катушки колебательного контура и ёмкость элементов контура, п - число пи.

Answer 2

Calculation of Inductance (L) in a Oscillatory Circuit

To determine the inductance (L) of the coil in the oscillatory circuit, we need to consider the given parameters:

- Frequency of the electromagnetic wave: 0.05 MHz - Area of the capacitor plates (S): 50 cm² - Dielectric constant of the dielectric material (E): 10 - Distance between the capacitor plates (d): 1 mm

The formula to calculate the inductance (L) in an oscillatory circuit is given by:

L = (1 / (ω² * C))

Where: - L is the inductance in henries (H) - ω is the angular frequency in radians per second (rad/s) - C is the capacitance in farads (F)

To calculate the inductance (L), we need to find the capacitance (C) first.

Calculation of Capacitance (C)

The capacitance (C) of a parallel plate capacitor can be calculated using the formula:

C = (E * ε₀ * S) / d

Where: - C is the capacitance in farads (F) - E is the dielectric constant of the material - ε₀ is the permittivity of free space (8.854 x 10⁻¹² F/m) - S is the area of the capacitor plates in square meters (m²) - d is the distance between the capacitor plates in meters (m)

Let's calculate the capacitance (C) first:

C = (E * ε₀ * S) / d

Substituting the given values: - E = 10 - ε₀ = 8.854 x 10⁻¹² F/m - S = 50 cm² = 0.005 m² - d = 1 mm = 0.001 m

C = (10 * 8.854 x 10⁻¹² F/m * 0.005 m²) / 0.001 m

Simplifying the equation: C = 44.27 x 10⁻¹² F

Now that we have the capacitance (C), we can calculate the inductance (L).

Calculation of Inductance (L)

The angular frequency (ω) can be calculated using the formula:

ω = 2πf

Where: - ω is the angular frequency in radians per second (rad/s) - f is the frequency in hertz (Hz)

Given the frequency is 0.05 MHz, we need to convert it to hertz:

f = 0.05 MHz = 0.05 x 10⁶ Hz

Now, let's calculate the angular frequency (ω):

ω = 2πf = 2π x 0.05 x 10⁶ rad/s

Substituting the value of ω and C into the formula for inductance (L):

L = (1 / (ω² * C))

L = (1 / ((2π x 0.05 x 10⁶ rad/s)² * 44.27 x 10⁻¹² F))

Calculating the value of L using the given formula:

**L ≈ 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000