Question

Електрон влітає в однорідне магнітне поле перпендикулярно його силовим лініям із швидкістю 109 см/с. Магнітна індукція поля дорівнює 20 мТл. Обчисліть радіус кола, яким рухатиметься електрон. Потрібен розв'язок ​

Answer 1

Ответ:

Объяснение:

Дано:

V = 1·10⁹ см/с = 1·10⁷ м/c

B = 20 мТл = 20·10⁻³ Тл

e = 1,6·10⁻¹⁹ Кл - модуль заряда электрона

m = 9,1·10⁻³¹ кг - масса электрона

________________

R - ?

Ларморовский радиус:

R = m·V / (e·B)

R = 9,1·10⁻³¹·1·10⁷ / (1,6·10⁻¹⁹·20·10⁻³) ≈ 2,8·10⁻³ м  или   2,8 мм

Answer 2

Calculation of the Radius of the Electron's Circular Path

To calculate the radius of the circular path along which the electron will move in a uniform magnetic field, we can use the equation for the centripetal force acting on a charged particle moving in a magnetic field.

The equation is as follows:

F = (mv^2) / r

Where: - F is the centripetal force acting on the electron - m is the mass of the electron - v is the velocity of the electron - r is the radius of the circular path

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

F = qvB

Where: - q is the charge of the electron - v is the velocity of the electron - B is the magnetic field strength

By equating these two equations, we can solve for the radius of the circular path:

(mv^2) / r = qvB

Simplifying the equation, we get:

r = (mv) / (qB)

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

Given: - Velocity of the electron (v) = 109 cm/s = 1.09 m/s - Magnetic field strength (B) = 20 mT = 0.02 T (1 T = 1 Tesla)

The mass of an electron (m) is approximately 9.11 x 10^-31 kg, and the charge of an electron (q) is approximately -1.6 x 10^-19 C.

Substituting these values into the equation, we get:

r = (9.11 x 10^-31 kg) x (1.09 m/s) / (-1.6 x 10^-19 C) x (0.02 T)

Calculating this expression gives us the radius of the circular path along which the electron will move.