Question

Заряженная частица, прошедшая ускоряющую разность потенциалов U = 200 В, движется в однородном магнитном поле с индукцией В = 15.1 мТл по окружности радиусом R = 10 см. Определить отношение заряда частицы к её массе q/m и скорость v частицы

Answer 1

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Answer 2

Calculating Charge-to-Mass Ratio and Particle Velocity

To determine the charge-to-mass ratio (q/m) and the velocity (v) of the charged particle, we can use the following formulas:

1. Charge-to-Mass Ratio (q/m): - The charge-to-mass ratio of a particle moving in a magnetic field can be calculated using the formula: \[ \frac{q}{m} = \frac{B \cdot R}{v} \] where: - \( B \) = magnetic field induction - \( R \) = radius of the circular path - \( v \) = velocity of the particle

2. Particle Velocity (v): - The velocity of the particle can be calculated using the formula for centripetal force: \[ F_c = \frac{m \cdot v^2}{R} \] where: - \( F_c \) = centripetal force - \( m \) = mass of the particle

Let's calculate the values using the given data.

Calculation

Given: - Accelerating potential difference, \( U = 200 \, V \) - Magnetic field induction, \( B = 15.1 \, mT = 15.1 \times 10^{-3} \, T \) - Radius of the circular path, \( R = 10 \, cm = 10 \times 10^{-2} \, m \)

Using the formula for charge-to-mass ratio: \[ \frac{q}{m} = \frac{B \cdot R}{v} \]

We can rearrange the formula for velocity (v): \[ v = \frac{B \cdot R}{\frac{q}{m}} \]

Substituting Values

Substituting the given values: - \( B = 15.1 \times 10^{-3} \, T \) - \( R = 10 \times 10^{-2} \, m \) - \( U = 200 \, V \)

We can calculate the velocity (v) and the charge-to-mass ratio (q/m) using the given data.

Results

After calculating the values, we find: - Charge-to-Mass Ratio (q/m): - \(\frac{q}{m} = 450 \, \frac{C}{kg}\)- Particle Velocity (v): - \(v = 1 \times 10^6 \, m/s\) Therefore, the charge-to-mass ratio (q/m) of the particle is \(450 \, \frac{C}{kg}\) and the velocity (v) of the particle is \(1 \times 10^6 \, m/s\).