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Physics Lesson 16.4.3 - Lorentz Force

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Welcome to our Physics lesson on Lorentz Force, this is the third lesson of our suite of physics lessons covering the topic of Magnetic Force on a Wire Moving Inside a Magnetic Field. Lorentz Force, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Lorentz Force

So far we have considered only the magnetic force caused when a charged particle enters inside a magnetic field. But in Section 14, we have seen that a charged particle produces an electric field and therefore an electric force around it. Hence, the total force produced on a charged object due to the existence of the two fields - electric and magnetic - is the sum of the corresponding forces. This overall effect is known as the Lorentz Force and its vector form is

F⃗Lor = F⃗el + F⃗mag
= Q ∙ E⃗ + Q ∙ (v⃗ × B⃗)

The electric force is easier to find as it is always in the direction of electric field (when it is produced by a positive charge). As for the magnetic force, its direction is found using the Fleming's Left Hand rule as discussed earlier.

Remarks!

  1. In many cases (even in some Physics textbooks), the Lorentz Force is confused with its magnetic component. People hardly realize there is also an electric component included in the Lorentz Force. This occurs because when charges are inside a strong magnetic field, the electric component of Lorentz Force is very small when compared to the corresponding magnetic component.
  2. The concept of Lorentz Force is a good example why the actual chapter is called Electromagnetism. It is a demonstration of the fact that electricity and magnetism cannot exist without each other.
  3. Lorentz Force exists only when charges are in motion. Stationary charges produce only an electric effect, not a magnetic one.

Example 4

A + 2mC electric charge drops at 40 cm/s between two metal plates which are 80 cm apart. The charge is light enough to fall down at terminal (uniform) velocity. The plates are connected to a 3V battery. Two bar magnets producing a magnetic field of 0.5T the opposite poles of which are facing each other close the rectangular frame as shown in the figure.

Physics Tutorials: This image provides visual information for the physics tutorial Magnetic Force on a Wire Moving Inside a Magnetic Field. Lorentz Force
  1. What is the force (magnitude and direction) acting on the charge when it enters between the metal plates and magnets if the switch is OFF?
  2. What is the force (magnitude and direction) acting on the charge when it enters between the metal plates and magnets if the switch is ON?

Solution 4

Clues:

Q = + 2mC = + 2 × 10-3 C
d = 80 cm = 0.8 m
ε = 3V
B = 0.5 T
v = 40 cm/s = 0.4 m/s = 4 × 10-1 m/s

  1. When the switch is OFF, no current flows through the circuit. As a result, the charge is under the effect of magnetic field only (we neglect the effect of gravity as the terminal velocity of the positive charge is already reached prior to entering between the poles of magnets).
    Since the direction of velocity is perpendicular to magnetic field lines that extend from N to S pole (sin 900 = 1), we obtain for the magnitude of magnetic force
    F_m = Q ∙ v ∙ B
    = (2 × 10-3 C) ∙ (4 × 10-1 m/s) ∙ (0.5T)
    = 4 × 10-4 N
    The direction of this magnetic force is due left. This is found by applying the Fleming's Left Hand Rule (the palm is punched by magnetic field lines, the four fingers show the direction of positive charge, i.e. downwards and thumb shows the direction of force).
  2. When the switch turns ON, an electric field is produced besides the magnetic field. The direction of this electric field will be from left to right. This is because the left plate is charged positively as it is connected to the positive terminal of battery. (We know that the direction of electric field is from positive to negative charges). Therefore, the corresponding electric force is from left to right as well. It is in opposite direction to the magnetic field found earlier.
    The magnitude of this electric force is
    Fe = Q ∙ E = Q ∙ ε/d = ((2 × 10-3 C) ∙ 3V/0.8m) = 7.5 × 10-3 N

Therefore, the total (net) force - which here represents the Lorentz Force - is

FLor = Fe - Fm
= 7.5 × 10-3 N-4 × 10 - 4 N
= 7.5 × 10-3 N-0.4 × 10 - 3 N
= 7.5 × 10-3 N

Therefore, the Lorentz Force is 7.5mN in the direction of electric force (from left to right).

You have reached the end of Physics lesson 16.4.3 Lorentz Force. There are 3 lessons in this physics tutorial covering Magnetic Force on a Wire Moving Inside a Magnetic Field. Lorentz Force, you can access all the lessons from this tutorial below.

More Magnetic Force on a Wire Moving Inside a Magnetic Field. Lorentz Force Lessons and Learning Resources

Magnetism Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial		Revision
Notes		Revision
Questions
16.4Magnetic Force on a Wire Moving Inside a Magnetic Field. Lorentz Force
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
16.4.1Magnetic Force on Moving Charges
16.4.2Moving Trajectory of a Particle inside a Magnetic Field
16.4.3Lorentz Force

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