Question

Из алюминиевой проволоки сечением 1мм кв сделано кольцо радиусом 10см. Перпендикулярно плоскости кольца за 0,01с включают магнитное поле с индукцией 0,01Тл. Найдите среднее значение индукционного тока, возникающего за это время в кольце? Пожалуйста, с полным расчетом и решением

Answer 1

Сопротивление кольца R=2пrp/s, 

где р - удельное сопр. металла.; s - сечение провода.

ЭДС E=(dB/dt)пr^2

Ток I=E/R=(dB/dt)rs/(2p).

Прошедший заряд q=Brs/(2p)

Средний ток Ia=q/t=Brs/(2pt)

Если не трудно, отметь пожалуйста как лучший ответ))

Answer 2

Calculation of the Average Induction Current in the Aluminum Ring

To find the average induction current in the aluminum ring, we can use Faraday's law of electromagnetic induction, which states that the induced electromotive force (emf) in a closed loop is equal to the rate of change of magnetic flux through the loop.

The formula for the induced emf is given by:

emf = -N * dΦ/dt

Where: - emf is the induced electromotive force, - N is the number of turns in the loop, - dΦ/dt is the rate of change of magnetic flux through the loop.

In this case, the aluminum ring is a single loop, so N = 1.

The magnetic flux through the loop is given by:

Φ = B * A

Where: - Φ is the magnetic flux, - B is the magnetic field strength, - A is the area of the loop.

Given: - The radius of the ring, r = 10 cm = 0.1 m, - The cross-sectional area of the wire, A = 1 mm² = 1 × 10^(-6) m², - The magnetic field strength, B = 0.01 T, - The time interval, dt = 0.01 s.

Let's calculate the average induction current using the above information.

Calculation:

Step 1: Calculate the area of the loop: A = π * r^2

Substituting the given value of r: A = π * (0.1)^2

Step 2: Calculate the magnetic flux: Φ = B * A

Substituting the given values of B and A: Φ = 0.01 * (π * (0.1)^2)

Step 3: Calculate the rate of change of magnetic flux: dΦ/dt = (Φ_final - Φ_initial) / dt

Since the magnetic field is perpendicular to the plane of the ring, the initial magnetic flux is zero.

Substituting the given value of dt: dΦ/dt = (Φ - 0) / 0.01

Step 4: Calculate the induced electromotive force (emf): emf = -N * dΦ/dt

Since N = 1: emf = -1 * (Φ - 0) / 0.01

Step 5: Calculate the average induction current: The induced emf is equal to the average induction current multiplied by the resistance of the loop. Since the resistance is not given, we cannot directly calculate the average induction current without additional information.

Please provide the resistance of the loop so that we can calculate the average induction current.