Question

Магнитный поток, пронизывающий катушку индуктивности L, равен Ф. Как изменится энергия магнитного поля если магнитный поток уменьшается в 4 раза а индуктивность увеличивается в 2 раза?

Answer 1

Ответ:

Уменьшится в 32 раза

Объяснение:

W=L*I²/2=ΔФ*I/2=ΔФ²/(2*I)

W1=ΔФ²/(2*L)

W2=(ΔФ/4)²/(2*2*L)=W1/32

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Answer 2

Calculation of Energy in a Magnetic Field

To determine how the energy of a magnetic field changes when the magnetic flux and inductance change, we can use the formula:

Energy (W) = 0.5 * L * I^2

Where: - W is the energy stored in the magnetic field - L is the inductance of the coil - I is the current flowing through the coil

In this case, the magnetic flux through the inductance coil is given as Ф. We are asked to determine how the energy changes when the magnetic flux decreases by a factor of 4 and the inductance increases by a factor of 2.

Let's assume the initial values are: - Magnetic flux (Ф) = Ф_initial - Inductance (L) = L_initial - Energy (W_initial) = 0.5 * L_initial * I^2

After the changes, the new values are: - Magnetic flux (Ф_new) = Ф_initial / 4 - Inductance (L_new) = L_initial * 2 - Energy (W_new) = 0.5 * L_new * I^2

To find the ratio of the new energy to the initial energy, we can divide the new energy by the initial energy:

W_new / W_initial = (0.5 * L_new * I^2) / (0.5 * L_initial * I^2)

Simplifying the equation, we find:

W_new / W_initial = L_new / L_initial

Therefore, the ratio of the new energy to the initial energy is equal to the ratio of the new inductance to the initial inductance.

Answer

If the magnetic flux through the inductance coil decreases by a factor of 4 and the inductance increases by a factor of 2, the energy of the magnetic field will also increase by a factor of 2.

Please note that this calculation assumes the current flowing through the coil remains constant. If the current changes, the energy calculation would be different.