Question

Зависимость силы тока от времени в колебательном контуре определяется уравнением i = 0,02sin500пt. Индуктивность катушки в контуре 0,1 Гн.Найти максимальную энергию магнитного поля и электрического поля

Answer 1

Уравнением контура задана амплитуда колебания тока:

Imax = 0.02 А = 20 мА ;

Максимальная энергия магнитного поля в контуре (в катушке) вычисляется, как:

WLmax = L Imax² / 2 ≈ 0.1*[2/100]²/2 = 20 / 1 000 000 = 20 мкДж ;

В процессе превращения энергии в колебательном контуре, в момент, когда ток будет равен нулю, вся энергия контура локализуется в ёмкостном элементе контура в виде энергии электрического поля.

Энергия электрического поля в этот момент будет максимальной, а в силу сохранения энергии в контуре, её значение будет таким же, каким оно было в тот момент, когда вся энергия контура была локализована в магнитеном поле. Т.е.

Wcmax = WLmax = LI²/2 ≈ 20 мкДж .

Answer 2

The Equation for Current in an Oscillating Circuit

The equation for the current in an oscillating circuit is given by i = 0.02sin(500πt), where i represents the current, t represents time, and π is a mathematical constant approximately equal to 3.14159. This equation describes the variation of current over time in the circuit.

Finding the Maximum Energy of the Magnetic Field

To find the maximum energy of the magnetic field in the circuit, we need to calculate the energy stored in the inductor. The energy stored in an inductor is given by the formula E = (1/2)Li^2, where E represents energy, L represents inductance, and i represents current.

In this case, the inductance of the coil is given as 0.1 H (henries). To find the maximum energy of the magnetic field, we need to determine the maximum current (i) in the circuit.

The equation for current in the circuit is i = 0.02sin(500πt). Since the maximum value of the sine function is 1, the maximum current (i) in the circuit is 0.02.

Substituting the values into the formula for energy, we have: E = (1/2)(0.1)(0.02)^2 = 0.00002 J (joules).

Therefore, the maximum energy of the magnetic field in the circuit is 0.00002 joules.

Finding the Maximum Energy of the Electric Field

To find the maximum energy of the electric field in the circuit, we need to calculate the energy stored in the capacitor. The energy stored in a capacitor is given by the formula E = (1/2)CV^2, where E represents energy, C represents capacitance, and V represents voltage.

In this case, the circuit is not explicitly mentioned to have a capacitor, so we cannot determine the maximum energy of the electric field without additional information about the circuit.

Please provide more information about the circuit or clarify if there is a capacitor present in the circuit, so that we can calculate the maximum energy of the electric field.