Question

Электрон влетает в магнитное поле (B=30тл) со скоростью 15км/с.найти радиус окружности по которой будет двигаться электрон , а так же кинетическую энергию электрона

Answer 1

На электрон действует сила Лоренца, по 2 заеону Ньютона
 Fл=еvB=ma=mv  в квадрате/R
mv в квадрате/R=еvB
mv /R=еB    R=mv/еВ  R=9,1*10 в минус 31 степени*15000/1,6*10 в минус 19 степени*30=2,8*10 в степени-9м
E=mv в квадрате/2  =9,1*10 в минус 31*15*15*10 в 6 степени/2=1,023*10 в 28 степени

Answer 2

Calculation of the Radius of the Electron's Circular Path

To find the radius of the circular path along which the electron will move in a magnetic field, we can use the formula for the centripetal force:

F = qvB

Where: - F is the centripetal force acting on the electron - q is the charge of the electron - v is the velocity of the electron - B is the magnetic field strength

In this case, the charge of an electron is -1.6 x 10^-19 C (coulombs), the velocity is 15 km/s (kilometers per second), and the magnetic field strength is 30 T (teslas).

Substituting the given values into the formula, we have:

F = (-1.6 x 10^-19 C) x (15,000 m/s) x (30 T)

Simplifying the equation, we get:

F = -7.2 x 10^-14 N

The centripetal force acting on the electron is -7.2 x 10^-14 N.

The centripetal force can also be expressed as:

F = (mv^2) / r

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

The mass of an electron is approximately 9.1 x 10^-31 kg.

Substituting the known values into the equation, we have:

-7.2 x 10^-14 N = (9.1 x 10^-31 kg) x (15,000 m/s)^2 / r

Simplifying the equation, we can solve for the radius:

r = (9.1 x 10^-31 kg) x (15,000 m/s)^2 / (-7.2 x 10^-14 N)

Calculating the value, we find:

r ≈ 3.02 x 10^-3 m

Therefore, the radius of the circular path along which the electron will move is approximately 3.02 x 10^-3 meters.

Calculation of the Kinetic Energy of the Electron

To find the kinetic energy of the electron, we can use the formula:

KE = (1/2)mv^2

Where: - KE is the kinetic energy - m is the mass of the electron - v is the velocity of the electron

Substituting the known values into the equation, we have:

KE = (1/2) x (9.1 x 10^-31 kg) x (15,000 m/s)^2

Calculating the value, we find:

KE ≈ 1.03 x 10^-16 J

Therefore, the kinetic energy of the electron is approximately 1.03 x 10^-16 joules.

Please note that the calculations provided are based on the given information and assumptions.