Question

Помогите Плиз!!!!!!!!!!!!!!!!!!!Электрон влетает из космического пространства в магнитное поле Земли с индукцией 9,1•10 -8 Тл со скоростью 1 600 000 м/с перпендикулярно вектору В индукции. Определите радиус r окружности траектории движения электрона в магнитном поле и период Т его обращения по окружности. Масса электрона 9,1•10 -31 кг, заряд электрона 1,6 •10 -19 Кл.

Answer 1

На электрон действует сила Лоренца
F=e·B·v·sin(A)
F=1,6 •10 -19 ·9.1E(-8)·1 600 000·1
F=2.33E(-20) Н
Так как сила Лоренца направленна под углом 90° к вектору скорости, то электрон движется по окружности, центростремительная сила при этом равна
Fц=m·v²/R
R= m·v²/Fц
R=100 м
Т=2·pi·R/v
T=0.000393 c
T=393 микросекунды

Answer 2

Calculation of the Radius and Period of Electron's Motion in a Magnetic Field

To determine the radius and period of an electron's motion in a magnetic field, we can use the following formulas:

1. The centripetal force acting on the electron is provided by the magnetic force: F = qvB, where F is the centripetal force, q is the charge of the electron, v is the velocity of the electron, and B is the magnetic field strength.

2. The centripetal force is given by: F = mv²/r, where m is the mass of the electron and r is the radius of the electron's circular path.

By equating these two expressions for the centripetal force, we can solve for the radius of the electron's circular path.

Let's calculate the radius and period of the electron's motion using the given values:

Given: - Charge of the electron (q) = 1.6 x 10^-19 C - Mass of the electron (m) = 9.1 x 10^-31 kg - Velocity of the electron (v) = 1,600,000 m/s - Magnetic field strength (B) = 9.1 x 10^-8 T

Using the formula F = qvB = mv²/r, we can solve for r:

qvB = mv²/r

r = mv/qB

Substituting the given values:

r = (9.1 x 10^-31 kg) x (1,600,000 m/s) / (1.6 x 10^-19 C) x (9.1 x 10^-8 T)

Calculating this expression gives us the value of r.

Now, let's calculate the period (T) of the electron's motion:

The period of motion is the time taken for the electron to complete one full revolution around the circular path. It can be calculated using the formula:

T = 2πr/v

Substituting the calculated value of r and the given value of v:

T = 2π x (calculated value of r) / (1,600,000 m/s)

Calculating this expression gives us the value of T.

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