Question

Электрон, ускоренный в однородном электрическом поле напряженностью Е=1,6 кВ/м, влетает в однородное магнитное поле с индукцией В=30 мТл и начинает двигаться по окружности радиусом R=2 мм. Какой путь прошел электрон в электрическом поле? Начальная скорость электрона равна нулю, масса электрона m=9,1×10-31 кг, заряд e= -1,6×10-19 Кл.

Answer 1

1) зная радиус найдем скорость электрона

R= m*V/q*B

V=R*q*B/m - скорость электрона
V= 2*10^-3*1.6*10^-19*30*10^-3/9,1*10^-31=10,67*10^6 м/с

2) работа по разгону электрона

A= E*q*L= m*V^2/2

L= m*V^2/2*E*q= 9*10^-31* 10.67^2*10^12/2*1,6*10^3*1,6*10^-19  (м)

Answer 2

Calculation of the Path Traveled by the Electron in the Electric Field

To calculate the path traveled by the electron in the electric field, we need to determine the force acting on the electron and use it to calculate the acceleration. With the acceleration, we can then calculate the time it takes for the electron to complete one revolution around the circle. Finally, we can use the time to calculate the distance traveled by the electron.

The force experienced by a charged particle in an electric field is given by the equation:

F = qE,

where F is the force, q is the charge of the particle, and E is the electric field strength.

In this case, the electric field strength is given as E = 1.6 kV/m and the charge of the electron is e = -1.6 × 10^-19 C.

Substituting the values into the equation, we have:

F = (-1.6 × 10^-19 C) × (1.6 × 10^3 V/m) = -2.56 × 10^-16 N.

Since the force is acting perpendicular to the velocity of the electron, it provides the necessary centripetal force to keep the electron moving in a circle.

The centripetal force is given by the equation:

F = m × a,

where m is the mass of the electron and a is the acceleration.

Rearranging the equation, we have:

a = F / m.

Substituting the values, we have:

a = (-2.56 × 10^-16 N) / (9.1 × 10^-31 kg) ≈ -2.81 × 10^14 m/s^2.

The negative sign indicates that the acceleration is directed towards the center of the circle.

Calculation of the Time Taken for One Revolution

The acceleration of the electron can be related to the velocity and radius of the circle using the equation:

a = v^2 / R,

where v is the velocity of the electron and R is the radius of the circle.

Rearranging the equation, we have:

v = sqrt(a × R).

Substituting the values, we have:

v = sqrt((-2.81 × 10^14 m/s^2) × (2 × 10^-3 m)) ≈ 2.51 × 10^5 m/s.

The time taken for one revolution can be calculated using the equation:

t = (2πR) / v.

Substituting the values, we have:

t = (2π × 2 × 10^-3 m) / (2.51 × 10^5 m/s) ≈ 3.99 × 10^-8 s.

Calculation of the Distance Traveled by the Electron

The distance traveled by the electron can be calculated using the equation:

d = v × t.

Substituting the values, we have:

d = (2.51 × 10^5 m/s) × (3.99 × 10^-8 s) ≈ 1.00 × 10^-2 m.

Therefore, the electron travels approximately 1.00 × 10^-2 meters in the electric field.

Please note that the calculations provided are based on the given values and assumptions.