Question

Даю 40 балов !!! Очень нужно решение задачи ( полностью с умовой) Між пластини влітає електрон із швидкістю 20 мм/с, направленою паралельно пластинам. На яку відстань від свого початкового напрямку змiститься електрон за час прольоту пластин? Відстань між пластинами 2 см, довжина - 5 см, рiзниця потенцiалiв мiж платинами 200 В.

Answer 1

Відповідь: 5,5 мм

Пояснення:

Answer 2

Problem Statement

You are given the following information: - An electron enters between two plates with a velocity of 20 mm/s, parallel to the plates. - The distance between the plates is 2 cm. - The length of the plates is 5 cm. - The potential difference between the plates is 200 V.

You need to find the distance by which the electron deviates from its initial direction during its flight between the plates.

Solution

To solve this problem, we can use the principles of electric fields and the motion of charged particles in electric fields.

The electric field between the plates can be calculated using the formula:

E = V / d

Where: - E is the electric field - V is the potential difference between the plates - d is the distance between the plates

Substituting the given values, we have:

E = 200 V / 2 cm = 100 V/cm

Now, we know that the force experienced by a charged particle in an electric field is given by:

F = q * E

Where: - F is the force - q is the charge of the particle - E is the electric field

The force experienced by the electron can be calculated using the formula:

F = e * E

Where: - e is the charge of an electron (1.6 x 10^-19 C)

Substituting the values, we have:

F = (1.6 x 10^-19 C) * (100 V/cm)

Now, we know that the force acting on the electron is perpendicular to its initial velocity. This force causes the electron to deviate from its initial path.

The acceleration experienced by the electron can be calculated using the formula:

F = m * a

Where: - F is the force - m is the mass of the electron (9.1 x 10^-31 kg) - a is the acceleration

Substituting the values, we have:

(1.6 x 10^-19 C) * (100 V/cm) = (9.1 x 10^-31 kg) * a

Simplifying the equation, we can solve for the acceleration:

a = (1.6 x 10^-19 C * 100 V/cm) / (9.1 x 10^-31 kg)

Now, we know that the distance traveled by the electron during its flight between the plates can be calculated using the formula:

d = v * t

Where: - d is the distance - v is the initial velocity of the electron - t is the time of flight

We need to find the time of flight. Since the force acting on the electron is perpendicular to its initial velocity, the electron will move in a circular path. The radius of this circular path can be calculated using the formula:

r = (m * v) / (q * B)

Where: - r is the radius of the circular path - m is the mass of the electron - v is the initial velocity of the electron - q is the charge of the electron - B is the magnetic field

In this case, the magnetic field is created by the electric field between the plates. The magnetic field can be calculated using the formula:

B = E / v

Substituting the values, we have:

B = (100 V/cm) / (20 mm/s)

Now, we can substitute the values of m, v, q, and B into the formula for the radius:

r = [(9.1 x 10^-31 kg) * (20 mm/s)] / [(1.6 x 10^-19 C) * (100 V/cm) / (20 mm/s)]

Simplifying the equation, we can solve for the radius:

r = (9.1 x 10^-31 kg * 20 mm/s) / (1.6 x 10^-19 C * 100 V/cm / 20 mm/s)

Now, we know that the time of flight can be calculated using the formula:

t = 2 * π * r / v

Substituting the values, we have:

t = 2 * π * [(9.1 x 10^-31 kg * 20 mm/s) / (1.6 x 10^-19 C * 100 V/cm / 20 mm/s)] / (20 mm/s)

Finally, we can substitute the values of v and t into the formula for the distance traveled by the electron:

d = v * t

Substituting the values, we have:

d = (20 mm/s) * [2 * π * [(9.1 x 10^-31 kg * 20 mm/s) / (1.6 x 10^-19 C * 100 V/cm / 20 mm/s)] / (20 mm/s)]

Simplifying the equation, we can solve for the distance traveled by the electron.

Please note that the above calculations are based on the given information and assumptions. If there are any additional factors or conditions not mentioned in the problem statement, the solution may vary.

I hope this helps! Let me know if you have any further questions.