Электричество и магнетизм · AP Physics C (Magnetism)
Симулятор силы Лоренца и движения заряженных частиц
Симулятор силы Лоренца и траектории заряженной частицы в магнитном поле: циклотрон
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- Вывод формул
- Режим проектора
- Печатный лист A4
Окно 3D симуляции● 60 FPS
Параметры эксперимента
×10⁶ m/s
T
Расчёты и показатели в реальном времени
Радиус орбиты r
--
Период обращения T
--
Величина силы Лоренца
--
Направление отклонения
--
Вывод формул в реальном времени
Основная формула:
--Подстановка значений:
--Физическое состояние: --
Разбор типовых задач и анализ экзаменационных ошибок
Worked Problem
Условие задачи: Proton (m=1.67*10^-27kg, q=1.6*10^-19C) enters B=0.1T at v=10^6 m/s. Find orbit radius and period.
Пошаговый вывод формул:
- r = mv/(qB) = 10.4cm. Period T = 2πm/(qB) = 0.656 μs.
Worked Problem
Условие задачи: Why does the Lorentz force do zero work on moving charges? Can it change particle velocity?
Пошаговый вывод формул:
- Force f = q(v x B) is always strictly perpendicular to velocity (cos 90° = 0), doing zero work. It alters velocity direction, not speed.
Рабочий лист для урока и домашние задания
Q1. Variant 1: When applying the Left-Hand Rule for negative charges (electrons), which direction must the 4 fingers point?
Answer Key: Opposite to electron velocity (along conventional current direction). Thumb then points to the true force vector.
Q2. Variant 2: What dictates max kinetic energy in a cyclotron? Increase accelerating voltage U or Dees radius R?
Answer Key: Ek,max = q²B²R²/(2m). Max energy depends strictly on B and Dee radius R, independent of accelerating voltage U.
Q3. Variant 3: What two stages comprise a mass spectrometer? How does it resolve chemical isotopes?
Answer Key: Velocity selector (v = E/B) + deflection magnetic chamber. Equal-speed isotopes trace radius r = mv/(qB) proportional to atomic mass m.
Часто задаваемые вопросы и типичные заблуждения
How to remember when to use the Left Hand vs Right Hand rule in electromagnetism?
Rule of thumb: "Force = Left Hand, Electricity Generation = Right Hand". Use left hand for forces (Ampere, Lorentz); right hand for induced currents.
If a charged particle travels parallel to magnetic field lines, does it experience a Lorentz force?
Zero force! f = qvB*sin(0°) = 0. The particle continues in an unperturbed straight line at constant velocity.
What spatial trajectory results if a charge enters a magnetic field at an oblique angle θ?
A helical helix orbit! The parallel velocity component drives uniform translation while perpendicular component traces circular orbits.
How does the geomagnetic field shield Earth from solar wind? How are auroras formed?
The magnetosphere deflects lethal solar cosmic particles via Lorentz forces, channeling them down polar lines to excite atmospheric atoms into glowing auroras.