Question

В однородном магнитном поле с индукцией 0,3 тл расположен проволочный виток так что плоскость перпендикулярна магнитному полю. Площадь охватываемая контуром витка равна 0,01 м2. Чему равна эдс индукции возникающая в витке при его повороте на угол 45 градусов? Время поворота рамки считать равным 1 с. Ответ выразите в милливольтах и округлите до десятых

Answer 1

Изначально поток вектора индукции магнитного поля равен Ф1=B*S
через время t поток вектора индукции магнитного поля равен Ф2=B*S*cos(45)
ЭДС=-(Ф2-Ф1)/t =B*S*(1-cos(45))/t = 0,3*0,01*(1-1/корень(2))/1 В =  0,00087868 В ~ 0,87868 мВ ~ 0,9 мВ

Answer 2

Calculation of the induced emf in the wire loop

To calculate the induced electromotive force (emf) in the wire loop when it is rotated at an angle of 45 degrees in a uniform magnetic field with an induction of 0.3 T, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced emf 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 wire loop - dΦ/dt is the rate of change of magnetic flux through the loop

In this case, we have a single wire loop, so N = 1.

To calculate the rate of change of magnetic flux, we need to determine the initial and final magnetic flux through the loop.

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

Φ = B * A * cos(θ)

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

In this case, the magnetic field induction B is 0.3 T, the area of the loop A is 0.01 m^2, and the angle θ is 45 degrees.

Let's calculate the initial and final magnetic flux through the loop:

Initial magnetic flux (Φ1) = B * A * cos(0) = 0.3 T * 0.01 m^2 * cos(0) = 0.003 T·m^2

Final magnetic flux (Φ2) = B * A * cos(45) = 0.3 T * 0.01 m^2 * cos(45) = 0.002121 T·m^2

Now, let's calculate the rate of change of magnetic flux (dΦ/dt):

dΦ/dt = (Φ2 - Φ1) / Δt

Where Δt is the time taken for the rotation, which is given as 1 second.

Substituting the values:

dΦ/dt = (0.002121 T·m^2 - 0.003 T·m^2) / 1 s = -0.000879 T·m^2/s

Finally, we can calculate the induced emf using the formula:

emf = -N * dΦ/dt = -1 * (-0.000879 T·m^2/s) = 0.000879 V

To express the answer in millivolts, we multiply by 1000:

emf = 0.000879 V * 1000 = 0.879 mV

Therefore, the induced emf in the wire loop, when it is rotated at an angle of 45 degrees in a uniform magnetic field with an induction of 0.3 T, is approximately 0.879 mV.

Answer

The induced electromotive force (emf) in the wire loop, when it is rotated at an angle of 45 degrees in a uniform magnetic field with an induction of 0.3 T, is approximately 0.879 mV.