Question

Горизонтальный проводник движется равноускоренно в вертикальном однородном магнитном поле, индукция которого равна 1 Тл. Скорость проводника направленна горизонтально, перпендикулярно проводнику. При начальной скорости проводника равной нулю и ускорении 8 м/с^2 он через некоторое время переместился на 1 м. ЭДС индукции на концах проводника в конце перемещения равна 6 В. Какова длина проводника ?

Answer 1

Так как проводник движется в магнитном поле, его ЭДС будет равно:
$\varepsilon = Bvl$
Путь пройденный проводником обозначим за $\Delta x$
В конце пути скорость будет равна:
$\Delta x=\cfrac{v^2-v_o^2}{2a}=\cfrac{v^2}{2a}\\v=\sqrt{2a\Delta x}$
Получаем:
$\varepsilon = Bl\sqrt{2a\Delta x}\\l=\cfrac{\varepsilon}{B\sqrt{2a\Delta x}}=1,5$
Ответ: 1,5 метра

Answer 2

Calculation of the Length of the Conductor

To calculate the length of the conductor, we can use the formula for the induced electromotive force (EMF) in a moving conductor in a magnetic field:

EMF = B * L * v

Where: - EMF is the induced electromotive force (in volts) - B is the magnetic field strength (in teslas) - L is the length of the conductor (in meters) - v is the velocity of the conductor (in meters per second)

In this case, the induced EMF is given as 6 V, the magnetic field strength is 1 T, and the velocity of the conductor is not provided. However, we are given that the conductor is moving with a constant acceleration of 8 m/s^2 and has traveled a distance of 1 m.

To find the velocity of the conductor, we can use the equation of motion:

v^2 = u^2 + 2 * a * s

Where: - v is the final velocity - u is the initial velocity (which is 0 in this case) - a is the acceleration - s is the distance traveled

Plugging in the values, we have:

v^2 = 0^2 + 2 * 8 * 1 v^2 = 16 v = 4 m/s

Now that we have the velocity, we can rearrange the formula for EMF to solve for the length of the conductor:

L = EMF / (B * v)

Plugging in the values, we have:

L = 6 / (1 * 4) L = 1.5 m

Therefore, the length of the conductor is 1.5 meters.