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 for the Electrons to Not Escape the Capacitor

To calculate the minimum voltage required for the electrons not to escape the capacitor, we can use the formula for the kinetic energy of an electron and the potential energy in an electric field.

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 potential energy in an electric field can be calculated using the formula: \[ P.E. = qV \] Where: - \( q \) = charge of the electron - \( V \) = potential difference

The minimum voltage required to prevent the electrons from escaping the capacitor can be found by equating the kinetic energy of the electrons to the potential energy in the electric field.

Calculation Steps

1. Calculate the kinetic energy of the electrons using the given potential difference of 5000 V. 2. Equate the kinetic energy to the potential energy and solve for the minimum voltage required.

Calculation

1. Kinetic energy of the electrons: - Given potential difference, \( V = 5000 \) V - The kinetic energy of the electrons can be calculated using the formula \( K.E. = \frac{1}{2}mv^2 \)

2. Equating kinetic energy to potential energy: - Equate the kinetic energy to the potential energy: \( K.E. = P.E. \) - Solve for the minimum voltage required, \( V \), to prevent the electrons from escaping.

Result

The minimum voltage required to prevent the electrons from escaping the capacitor can be calculated using the above steps.

Let's proceed with the calculation.