Question

Чему равна скорость альфа-частицы, влетевшей в однородное магнитное поле с индукцией B= 1 Тл в направлении, перпендикулярном вектору индукции, если в магнитном поле она движется по окружности радиусом 5 мм?

Answer 1

B = 1 Тл
$\alpha =90 ^{o}$
R = 5 мм = $5*10 ^{-3}$ м
$q = 3,2*10 ^{-19}$ Кл
$m = 6,6*10 ^{-27}$ кг
$v-?$
продолжение у файле....

Answer 2

Calculating the Speed of an Alpha Particle in a Magnetic Field

To calculate the speed of an alpha particle moving in a magnetic field, we can use the formula for the centripetal force acting on the particle.

Given: - Magnetic field induction, B = 1 T - Radius of the circular path, r = 5 mm

Formula for Centripetal Force in a Magnetic Field

The centripetal force acting on a charged particle moving in a magnetic field is given by the formula: F = qvB

Where: - F = Centripetal force - q = Charge of the particle - v = Velocity of the particle - B = Magnetic field induction

Centripetal Force and Velocity

The centripetal force can also be expressed as F = mv^2/r, where m is the mass of the particle and r is the radius of the circular path.

Equating the two expressions for centripetal force, we get: mv^2/r = qvB

Solving for v, we find: v = qBr/m

Substituting Known Values

- The charge of an alpha particle, q, is twice the elementary charge, so q = 2e. - The mass of an alpha particle, m, is approximately 4 times the mass of a proton, so m = 4mp.

Substituting these values into the equation, we get: v = (2eBr)/(4mp)

Calculation

Let's calculate the speed of the alpha particle using the given values.

Using the given magnetic field induction, B = 1 T, and the radius of the circular path, r = 5 mm, we can calculate the speed of the alpha particle.

e is the elementary charge, and mp is the mass of a proton.

Answer

The speed of the alpha particle, v, can be calculated using the formula: v = (2eBr)/(4mp)

Let's calculate the value of v using the given values.