Question

Катушка сопротивлением 100 Ом, состоящая из 1000 витков, внесена в однородное магнитное поле. Площадь поперечного сечения каждого витка равна 5 см. В течение некоторого времени индукция магнитного поля уменьшилась с 0,8 Тл до 0,3 Тл. Какой заряд индуцирован в проводнике за это время?

Answer 1

Q=I*Δt

ток можно найти по закону Ома I=e/R
где е1=-ΔФ/Δt   ЭДС индукции

е= N*ΔB*S/Δt=-S*(B2-B1)*N/Δt=S*(B1-B2)*N/Δt

Q=S*(B1-B2)*N/R=5*10^-4*(0,8-0,3)*1000/100=25*10^-4 Кл

Answer 2

Q=N•S•(B1-B2)/R=2,5 мКл.

R=100 Ом – сопротивление катушки
N=1000 – число витков
S=5 см²=5•10^(-4) м² - площадь сечения катушки
B1=0,8;B2=0,3 Тл – начальное и конечное значения индукции магнитного поля

Q - ?заряд, прошедший через катушку

Согласно закону электромагнитной индукции Фарадея

Q=ΔΨ/R,гдеΨ=N•Φ - потокосцепление катушки,

Φ=B•S - магнитный поток через катушку.

ТогдаΨ=N•B•S,ΔΨ=N•S•ΔB=N•S•(B1-B2)

Окончательно: Q=N•S•(B1-B2)/R

Подставим численные значения:

Q=1000•5•10^(-4) м²•(0,8-0,3)/100=2,5•10^(-3) Кл=2,5 мКл.

Answer 3

Calculation of Induced Charge in the Conductor

To calculate the induced charge in the conductor, we need to use Faraday's law of electromagnetic induction. According to Faraday's law, the induced electromotive force (emf) in a closed loop is equal to the rate of change of magnetic flux through the loop.

The formula to calculate the induced emf is:

emf = -N * dΦ/dt

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

In this case, the coil has a resistance of 100 Ω and consists of 1000 turns. The area of the cross-sectional area of each turn is 5 cm². The magnetic field decreases from 0.8 T to 0.3 T over a certain period of time.

To calculate the induced charge, we need to find the induced emf and then divide it by the resistance of the coil using Ohm's law.

Calculation Steps:

1. Calculate the initial and final magnetic flux through the coil. 2. Calculate the rate of change of magnetic flux. 3. Calculate the induced emf using Faraday's law. 4. Calculate the induced charge using Ohm's law.

Let's perform these calculations step by step.

Step 1: Calculate the Initial and Final Magnetic Flux

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

Φ = B * A

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

Given that the initial magnetic field is 0.8 T and the final magnetic field is 0.3 T, and the area of each turn is 5 cm², we can calculate the initial and final magnetic flux.

Initial magnetic flux (Φ₁) = 0.8 T * 5 cm² Final magnetic flux (Φ₂) = 0.3 T * 5 cm²

Step 2: Calculate the Rate of Change of Magnetic Flux

The rate of change of magnetic flux is given by the formula:

dΦ/dt = (Φ₂ - Φ₁) / Δt

Where: - dΦ/dt is the rate of change of magnetic flux - Φ₂ is the final magnetic flux - Φ₁ is the initial magnetic flux - Δt is the change in time

Since the time interval is not provided in the question, we cannot calculate the rate of change of magnetic flux.

Step 3: Calculate the Induced EMF

Using Faraday's law, the induced emf is given by the formula:

emf = -N * dΦ/dt

Since we cannot calculate the rate of change of magnetic flux, we cannot calculate the induced emf.

Step 4: Calculate the Induced Charge

Finally, to calculate the induced charge, we need to divide the induced emf by the resistance of the coil using Ohm's law:

Q = emf / R

Since we cannot calculate the induced emf, we cannot calculate the induced charge.

Unfortunately, without the time interval or the rate of change of magnetic flux, we cannot determine the induced charge in the conductor.