Lessons 55–56 · 2 lessons · P.Q. Habibullayev, A. Boydedayev, A.D. Bahromov, J.E. Usarov, K.T. Suyarov, M.K. Yuldasheva. Physics, textbook for Grade 8 of general secondary schools, revised and enlarged 3rd edition. “O‘qituvchi” Publishing and Printing Creative House, Tashkent, 2019
56
Motion of a charged particle in a magnetic field
Textbook: pp. 155–156
GoalKnow the force of a magnetic field on a moving charge — the Lorentz force F = qvB — and its direction.
New words
Lorentz force · Lorens kuchicharged particle · zaryadli zarravelocity · tezlikelementary charge e · elementar zaryad e
Explanation
A magnetic field also acts on a moving charged particle; this force is called the Lorentz force. If the particle’s velocity v is perpendicular to the field lines, F = q·v·B: q is the charge, v the velocity, B the magnetic induction. The force direction is found with the left-hand rule (four fingers along the velocity of a positive particle; for a negative particle the four fingers are held opposite to the velocity). Since the Lorentz force is always perpendicular to the velocity, it changes only the direction of the particle’s velocity, not its value. The Ampère force is in fact the sum of Lorentz forces on the many moving charges in the conductor. For an electron e = 1.6·10⁻¹⁹ C.
Worked examples
An electron with v = 2·10⁷ m/s in B = 1.25 T, q = 1.6·10⁻¹⁹ C: F = 1.6·10⁻¹⁹ · 2·10⁷ · 1.25 = 4·10⁻¹² N = 4 pN.
A particle with q = 2·10⁻⁶ C, v = 100 m/s, B = 0.5 T: F = 2·10⁻⁶ · 100 · 0.5 = 10⁻⁴ N. If B doubles, F doubles too.
Class activity
Draw in your notebook an electron beam entering a magnetic field (field lines entering the page) and mark the force direction with the left-hand rule (remember the electron is negative).
Practice
1
Write the formula for the Lorentz force and name its quantities.
F = qvB: q is the charge, v the velocity, B the induction (v perpendicular to the field).
2
An electron with v = 10⁷ m/s in B = 2.5 T. F in pN? (e = 1.6·10⁻¹⁹ C)
4
3
A particle with q = 5·10⁻⁶ C, v = 200 m/s, B = 0.2 T. F in µN? (1 N = 10⁶ µN)
200
4
Why does the Lorentz force not change the speed of a particle?
It is always perpendicular to the velocity, so it does no work and changes only the direction.