Question

Кругле кільце радіуса 10 см знаходиться в перпендикулярному до його площини однорідному магнітному полі з індукцією 0,1 Тл. Поле вимикають, відтак індукція спадає до нуля за час 10 мс. Визначити середню напруженість електричного поля в кільці (В/м), що виникає при цьому

Answer 1

Відповідь: 0,5 В/м

Пояснення:

Answer 2

Calculation of the Average Electric Field in the Ring

To determine the average electric field in the ring, we need to consider Faraday's law of electromagnetic induction. According to this law, a changing magnetic field induces an electric field. In this case, when the magnetic field is switched off, the change in magnetic field induces an electric field in the ring.

The formula to calculate the average electric field induced in the ring is given by:

E_avg = -ΔΦ/Δt

Where: - E_avg is the average electric field in the ring, - ΔΦ is the change in magnetic flux through the ring, and - Δt is the time taken for the change in magnetic field.

To calculate the change in magnetic flux, we need to know the initial and final magnetic flux through the ring.

Calculation of the Change in Magnetic Flux

The magnetic flux through a closed loop is given by the formula:

Φ = B * A * cos(θ)

Where: - Φ is the magnetic flux, - B is the magnetic field strength, - A is the area of the loop, and - θ is the angle between the magnetic field and the normal to the loop.

In this case, the magnetic field is perpendicular to the plane of the ring, so the angle θ is 90 degrees. Therefore, the formula simplifies to:

Φ = B * A

The initial magnetic flux through the ring is given by:

Φ_initial = B_initial * A

And the final magnetic flux through the ring is:

Φ_final = B_final * A

Since the magnetic field is switched off, the final magnetic field strength B_final is zero.

Calculation of the Average Electric Field

Now that we have the initial and final magnetic flux through the ring, we can calculate the change in magnetic flux:

ΔΦ = Φ_final - Φ_initial = B_final * A - B_initial * A = -B_initial * A

The negative sign indicates that the change in magnetic flux is opposite to the initial magnetic flux.

We also know that the time taken for the change in magnetic field is 10 ms, which is equivalent to 0.01 seconds.

Using the formula for the average electric field, we can calculate:

E_avg = -ΔΦ/Δt = -(-B_initial * A) / 0.01 = B_initial * A / 0.01

Calculation of the Average Electric Field Value

To calculate the average electric field value, we need to know the initial magnetic field strength B_initial and the area of the ring A.

From the given information, the initial magnetic field strength is 0.1 T and the radius of the ring is 10 cm, which is equivalent to 0.1 m.

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

A = π * r^2

Substituting the values, we get:

A = π * (0.1)^2 = 0.01π m^2

Now we can calculate the average electric field:

E_avg = B_initial * A / 0.01 = 0.1 * 0.01π / 0.01 = 0.1π V/m

Therefore, the average electric field in the ring is 0.1π V/m.

Please note that the value of π is approximately 3.14159.

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