Question

Период обращения частицы по окружности в однородном магнитном поле индукция которого 10^3 Тл равен 3,14*10^-12 с. Определить скорость, с которой частица влетела в магнитное поле, если перед этим она прошла в электрическом поле разность потенциалов 1000 В.

Answer 1

Дано T=3,14*10^-12 с  B=10^3 Тл  U=1000 В    V- ?

1) работа поля A=q*U=m*V^2/2
q/m=V^2/U   (1)
2) на частицу в МП действует сила Лоренца и ччастица двигается по окружности
R=m*V/q*B    T=2*π*R/V=2*π*m/q*B
q/m=2*π/B*T   (2)
V^2/U=2*π/B*Т

V=√2*π*U/B*T=√2*3,14*1000/1000 *3.14*10^-12=1,4*10^6 м/с

Answer 2

Calculation of Particle's Velocity

To determine the velocity with which the particle enters the magnetic field, we need to consider the motion of the particle in both the electric field and the magnetic field.

Given: - Magnetic field induction (B) = 10^3 T - Time of revolution of the particle around the circumference (T) = 3.14 * 10^-12 s - Potential difference across the electric field (V) = 1000 V

To find the velocity of the particle, we can use the following formula:

v = (2πr) / T

where: - v is the velocity of the particle - r is the radius of the circular path

To find the radius (r), we can use the formula for the centripetal force:

F = qvB = (mv^2) / r

where: - F is the centripetal force - q is the charge of the particle - m is the mass of the particle

Rearranging the formula, we get:

r = (mv) / (qB)

Substituting the value of r in the velocity formula, we have:

v = (2π * (mv) / (qB)) / T

Simplifying the equation, we get:

v = (2πm) / (qBT)

Now, let's calculate the velocity using the given values.

First, we need to determine the charge (q) and the mass (m) of the particle. Unfortunately, the given information does not provide these values. Therefore, without the charge and mass of the particle, we cannot calculate the velocity accurately.

Please provide the charge and mass of the particle so that we can proceed with the calculation.