Question

Поток электронов, получивших свою скорость в результате прохождения разности потенциалов 5000 В, влетает в середину плоского конденсатора. Какое наименьшее напряжение нужно приложить к пластинам конденсатора, чтобы электроны не вылетели из него? Размеры конденсатора: длина 5 см, расстояние между пластинами 1 см.

Answer 1

Дано
∆φ = 5000 B
L = 5 см
d = 1 см
найти
U
решение
Ek = q∆φ
mV^2/2 =q∆φ
V^2 = q/m * 2∆φ
V = √(q/m * 2∆φ)
время пролета  t = L/V = L/√(q/m * 2∆φ)
t^2 = L^2/(q/m * 2∆φ)    (1)
поток влетает в середину плоского конденсатора h =d/2
движение от середины к обкладке+
h = at^2/2                    (2)
сила на электрон в поле конденсатора
F = Eq = U/h *q
ускорение  a =F/m = U/h *q/m   (3)
подставляем  (1)(3) в (2)
h = U/h *q/m * L^2/(q/m * 2∆φ)/2  =U*L^2/(4h∆φ)
U = (4h^2∆φ) /L^2 = (4(d/2)^2∆φ) /L^2 =  ∆φ *(d/L)^2
U = 5000 *(1/5)^2 = 200 B

ответ 200 В

Answer 2

Calculating the Minimum Voltage Required to Prevent Electrons from Exiting the Capacitor

To calculate the minimum voltage required to prevent electrons from exiting the capacitor, we can use the formula for the kinetic energy of an electron and the energy gained from passing through a potential difference.

The kinetic energy of an electron can be calculated using the formula: \[ K.E. = \frac{1}{2}mv^2 \] Where: - \( m \) = mass of the electron - \( v \) = velocity of the electron

The energy gained from passing through a potential difference can be calculated using the formula: \[ \Delta E = qV \] Where: - \( \Delta E \) = energy gained - \( q \) = charge of the electron - \( V \) = potential difference

The minimum voltage required to prevent electrons from exiting the capacitor can be calculated by equating the kinetic energy of the electrons to the energy gained from passing through the potential difference.

Given Parameters

- Potential difference (\( V \)) = 5000 V - Length of the capacitor (\( l \)) = 5 cm = 0.05 m - Distance between the plates (\( d \)) = 1 cm = 0.01 m

Calculating the Velocity of Electrons

The velocity of the electrons can be calculated using the formula: \[ v = \sqrt{\frac{2K.E.}{m}} \]

Calculating the Charge of the Electron

The charge of the electron is \( e = 1.6 \times 10^{-19} \) C.

Calculating the Minimum Voltage

The minimum voltage required to prevent electrons from exiting the capacitor can be calculated using the formula: \[ V = \frac{K.E.}{e} \]

Let's calculate the minimum voltage required.