Question

В направлении,перпендикулярном линиям индукции,влетает в магнитное поле электрон со скоростью 10Мм/с.Найти индукцию поля,если электрон описал в поле окружность радиусом 1 см.

Answer 1

Сила Лоренца, действующая на движущийся заряд со стороны МП сообщает частице центростремительное ускорение
$m \frac{v ^{2} }{R} =qvB$
$B= \frac{mv}{qR}$
для электрона
$m=9.1*10 ^{-31} kg$
$q=1.6*10 ^{-19} Kl$
В СИ
$v=10 ^{7} m/s$
$R=0.01m$ 
$B= \frac{9.1*10 ^{-31} *10 ^{7} }{1.6*10 ^{-19} *10 ^{-2} } =5.69*10 ^{-3} Tl=5.7mTl$  Ответ

Answer 2

Calculation of Magnetic Field Induction

To find the magnetic field induction (B) when an electron enters a magnetic field perpendicular to the lines of induction, we can use the formula for the magnetic force experienced by a charged particle moving in a magnetic field.

The formula for the magnetic force (F) experienced by a charged particle moving in a magnetic field is given by:

F = qvB

Where: - F is the magnetic force - q is the charge of the particle - v is the velocity of the particle - B is the magnetic field induction

In this case, the charged particle is an electron with a charge of -1.6 x 10^-19 C (coulombs) and a velocity of 10 Mm/s (megameters per second). The electron moves in a circular path with a radius of 1 cm (centimeter).

To find the magnetic field induction (B), we can rearrange the formula as follows:

B = F / (qv)

Since the electron moves in a circular path, the magnetic force (F) provides the necessary centripetal force to keep the electron in its circular path. The centripetal force (Fc) is given by:

Fc = (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 (m) is approximately 9.11 x 10^-31 kg.

Substituting the values into the formula for centripetal force, we have:

F = Fc = (mv^2) / r

Substituting the values into the formula for magnetic field induction, we have:

B = F / (qv) = (mv^2) / (qvr)

Now we can calculate the magnetic field induction (B) using the given values.

Calculation:

Given: - Charge of the electron (q) = -1.6 x 10^-19 C - Velocity of the electron (v) = 10 Mm/s = 10 x 10^6 m/s - Radius of the circular path (r) = 1 cm = 0.01 m - Mass of the electron (m) = 9.11 x 10^-31 kg

Using the formula for magnetic field induction:

B = (mv^2) / (qvr)

Substituting the given values:

B = (9.11 x 10^-31 kg) x (10 x 10^6 m/s)^2 / (-1.6 x 10^-19 C x 0.01 m x 9.11 x 10^-31 kg)

Calculating the value:

B = 5 T (Tesla)

Therefore, the magnetic field induction is 5 Tesla.