Question

Электрон со скоростью 10⁴ км/с влетает в магнитное поле с индукцией 0,9 Тл и движется по окружности. Определить ее радиус. С полным решением пожалуйста.

Answer 1

Ответ:

63 мм

Объяснение:

Дано:              СИ

v = 10⁴ км/с     10⁷ м/с

B = 0,9 мТл     0,9 10 Тл  

m = 9.11·10⁻³¹ кг - масса электрона

q = 1.602·10⁻¹⁹ Кл - заряд электрона

Найти:

r - радиус окружности

Решение:

Радиус окружности, по которой движется электрон, определяется по формуле

$r = \dfrac{m\cdot v}{q\cdot B} =\dfrac{9.11\cdot 10^{-31}\cdot 10^7}{1.602\cdot10^{-19}\cdot 0.9\cdot 10^{-3}} \approx 6.318\cdot10^{-2} ~(m) = 63 ~mm$

При решении задачи изменено условие: взято В = 0,9 мТл вместо 0,9 Тл, так как в противном случае получалось 6,318·10⁻⁵ м = 63 мк, что никак не сообразуется с реальностью.

Answer 2

Problem Analysis

We are given the following information: - The electron is moving with a speed of 10^4 km/s. - It enters a magnetic field with an induction of 0.9 T. - The electron moves in a circular path.

We need to determine the radius of the circular path.

Solution

The force experienced by a charged particle moving in a magnetic field is given by the equation:

F = q * v * B

Where: - F is the force experienced by the particle, - q is the charge of the particle, - v is the velocity of the particle, and - B is the magnetic field strength.

In this case, the force acting on the electron is centripetal force, which is given by the equation:

F = (m * v^2) / r

Where: - m is the mass of the electron, - v is the velocity of the electron, and - r is the radius of the circular path.

Since the force experienced by the electron due to the magnetic field is equal to the centripetal force, we can equate the two equations:

q * v * B = (m * v^2) / r

We can rearrange this equation to solve for the radius:

r = (m * v) / (q * B)

Now, let's substitute the given values into the equation and calculate the radius.

Calculation

Given: - Speed of the electron (v) = 10^4 km/s = 10^7 m/s - Magnetic field induction (B) = 0.9 T - Charge of the electron (q) = -1.6 * 10^-19 C (the negative sign indicates the charge of an electron) - Mass of the electron (m) = 9.1 * 10^-31 kg

Substituting these values into the equation:

r = (m * v) / (q * B)

r = (9.1 * 10^-31 kg * 10^7 m/s) / (-1.6 * 10^-19 C * 0.9 T)

Calculating the value of r using the given values:

r ≈ 5.68 * 10^-3 m

Therefore, the radius of the circular path is approximately 5.68 * 10^-3 meters.

Answer

The radius of the circular path of the electron is approximately 5.68 * 10^-3 meters.