# What is Lorentz force: Definition and 197 Discussions

In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge q moving with a velocity v in an electric field E and a magnetic field B experiences a force of

F

=
q

E

+
q

v

×

B

{\displaystyle \mathbf {F} =q\,\mathbf {E} +q\,\mathbf {v} \times \mathbf {B} }
(in SI units). It says that the electromagnetic force on a charge q is a combination of a force in the direction of the electric field E proportional to the magnitude of the field and the quantity of charge, and a force at right angles to the magnetic field B and the velocity v of the charge, proportional to the magnitude of the field, the charge, and the velocity. Variations on this basic formula describe the magnetic force on a current-carrying wire (sometimes called Laplace force), the electromotive force in a wire loop moving through a magnetic field (an aspect of Faraday's law of induction), and the force on a moving charged particle.
Historians suggest that the law is implicit in a paper by James Clerk Maxwell, published in 1865. Hendrik Lorentz arrived at a complete derivation in 1895, identifying the contribution of the electric force a few years after Oliver Heaviside correctly identified the contribution of the magnetic force.

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1. ### Ion moving through electric potential difference and magnetic field

My question is about item (b). For item (a) we have uniform circular motion in the regions with uniform magnetic field. $$\vec{F}_{B_1}=qv\hat{\theta}_1\times B_1(-\hat{k})=-qv_1B_1\hat{r}_1=-mR_1\theta'^2\hat{r}_1\tag{1}$$ $$B_1=\frac{mv_1}{R_1q}\tag{2}$$ A similar calculation for the...
2. ### How to simplify \nabla (A.v) in the derivation of Lorentz force?

I know that ##∇(A⋅v)=(A⋅∇)⋅v+(v⋅∇)⋅A+v×(∇×A)+A×(∇×v)## The third term ##v×(∇×A)## simplifies to ##v×B##. I'm just now sure how to "get rid" of the other terms. I tried checking for some vector identities but couldn't make any headways. Any guidance?
3. ### I Why are Maxwell's equations and the Lorentz force "so different"

Hi. Maxwell's equations tell us how charges and currents act on electric and magnetic fields. However, when we conversely want to investigate how EM fields act charges and currents, we need this very different thing called Lorentz force. This all looks so asymmetric to me because those laws...
4. ### I Question on the Lorentz force: Why is the force not F=q(v×B) = F=qv×qB

Background: is the equation of Lorentz force for the force acting on a moving charge in electric and magnetic field. For the magnetic field only it is : F=qv×B. Question: For magnetic field only why is the force not F=q(v×B) = F=qv×qB
5. ### Lorentz Force In Capacitors

I am searching online for resources regarding studies done on the effect of the Lorentz force due to short circuit faults in capacitors. Although a DC-link capacitor only sees the ripple, there would be high current during a fault. Since F=(qE + JxB), I am curious what the effects of the high...
6. ### I Molten metal flow due to high currents

It is mentioned in the book "Ampere-Neumann Electrodynamics of Metals", Peter Graneau, that Carl Hering in 1923 operated furnaces by passing high current through the molten metal pool. He observed molten metal flow due to the currents. How is the conductor motion explained?
7. ### I What types of forces are described in the standard minimal QED Lagrangian?

In Q.E.D., the electrical part of the Lorentz Force between unlike and like charged particles is realized through the absorption and emission of photons. How is the magnetic part of the Lorentz Force realized in Q.E.D. via photon activity? As always, thanks in advance.
8. ### Using Lorentz Force to derive V = E/B

Suppose the E-field is ##-E_y\hat y##, and B-field is ##B\hat z##. Mass is ##m##. z | |_____x / y ##m(\ddot x \hat x + \ddot y \hat y) = q(-E_y \hat y + (v_x \hat x + v_y \hat y) \times B \hat z)## By grouping terms with ##\hat x## and ##\hat y## together, ##m\ddot x = -qv_yB##...
9. ### Maxwell Equations, Lorentz Force and Coulumb Force

Here the 3 set of equations we know, the Maxwell Equations, Lorentz Force, and Coulumb Force, actually I doubt a lot what set of equations represent all the electromagnetic aspects, I try research over the internet and I found a lot of contradictions in the answers, someone says we can get the...
10. ### Lorentz force acting upon an electron moving in a circle

So as the summary suggests, I am studying Electromagnetism, magnetic properties of matter and Magnetization vector in particular. As a first example and to introduce the Magnetization vector (M), my textbook shows a ferromagnetic substance in a uniform magnetic field (B). Then, every atom of...
11. ### Confusion about the right hand rule (Lorentz Force)

Hello. I am trying to do a basic experiment to demonstrate I⊗β≈ƒ or current cross magnetic field results in a force perpendicular to the plane of the other two. But every time I test this out, it appears I get a force in the same direction as the magnetic field. Here is my experiment: Strong...
12. ### Best straightforward method to calculate the direction of the Lorentz force

Hi guys, I'm being introduced to magnetism, and the direction of the Lorentz force is quite confusing since it's involving a vector product. Which method would you recommend me in order to easily deduce the direction?
13. ### Magnetic attraction / repulsion from the Lorentz force

I'm trying to understand how the Lorentz force can explain why magnets attract and repel. The explanations that I have found have mostly involved the magnets moving in a way that decreases the forces between them ( ) but I have not been able to find any intuitive explanation involving the...
14. ### I Lorentz Force Equation: Coercion & Maxwell Stress Tensor

When deriving the Maxwell Stress tensor, the Lorentz formula is converted from point particle: F=qE+qv x B Into current and charge density: F=ρ E + j x B However an argument can be made that we can't "fieldify" both q and E at one step, and thus, a "coercion" of the field to a value is...
15. ### The Lorentz Force Law Can be Completely Inaccurate

If you take a bar magnet and place a wire with current a short distance from the end, Lorentz's law can be used to accurately predict the location and magnitude of the resulting forces. The same is true if you use a large volume uniform magnetic field to create an induced field in a bar ferrite...
16. ### How Do You Calculate Forces when The Lorentz Force Doesn't Seem to Apply?

If the mu of the ferrite is high, as suggested, the B field on that section of wire is zero, and therefore there is no force on the wire. Instead there is a comparable force on the ferrite itself. But suppose you allow the ferrite to have different values of mu. If mu=1 the force is just...
17. ### Equation of motion in polar coordinates for charged particle

A solution of equations of motion for charged particle in a uniform magnetic field are well known (##r = const##, ## \dot{\phi} = const##). But if I tring to solve this equation using only mathematical background (without physical reasoning) I can't do this due to entaglements of variables...
18. ### Lorentz force between two moving charges

Two charges are moving mutually perpendicular to each other in space with constant velocities. The moment one charge crosses over the line of path of second charge the force on 1st charge (located just behind the 2nd charge moving away from it) appear to be zero (Magnetic field due to 2nd...
19. ### Why is the Lorentz force linear with velocity?

I am working on derivation of Lorentz force. (I know that Lorentz force is in some sense definition of fields, but still there is nontrivial dependence on velocity). I want to derive that the force is linear in components of velocity, so for example $$F_x=q(E+Av_x + Bv_y + Cv_z ),$$where ##A...
20. ### Reaction Force of Lorentz Force

Hi everyone, in school we recently learned about the Lorentz Force, which says that when charged particles move through an electric field (perpendicular to the field lines), a force is excerted on them (called the Lorentz Force), which goes perpendicular to both the magnetic field lines and the...
21. ### Detecting Lorentz Force: Experiment with Strong Neodymium Magnet

I setup an experiment to detect a magnetic field due to the Lorentz force acting on a current. It is a hollow conducting cylinder with a magnet at one end. With current flowing in the cylinder I approach the negative end with the north pole of the magnet. Using the left hand rule I expected the...
22. ### Conceptual difference between a motor and a generator

Hi. In order to explain the motion of an (accelerating) electromotor, we need the Lorentz force which itself is not one of Maxwell's equations. Conversely, if we use the same electromotor inversely to generate electricity, Faraday's law (which is a Maxwell's equation) and the resistance of the...
23. ### Is the Lorentz magnetic force verified?

Can someone provide me with some original experiments conducted which verified the Lorentz magnetic force : F = q(v X B). Google does not give me any links except to explanations of the Lorentz force law.
24. ### Interesting Magnetic Field Induction Problem

Homework Statement Suppose we have an isolated, long, narrow straight wire with low electrical resistivity. A constant current ##I## is sent through this wire. We know that if an electron is sent on a path which is perpendicular to the wire, towards it, with an initial speed ##v_0##, and the...
25. ### Nullifying Lorentz Force on Proton Moving in Parallel Direction

Homework Statement A proton moves with a speed ##v = 3 \cdot 10^5 \frac{m}{s}## in the parallel direction to ##i+k##. A magnetic field of ##1T##, in the ##i+j+k## acts over it. Which electric field must we apply in this region so that the Lorentz force over the proton is null? Homework...
26. ### Magnetic Lorentz Force: Questions & Answers

Magnetic Lorentz force is the force experienced by any charged particle moving in a magnetic field.i want to clarify some doubts regarding this topic of Magnetic Lorentz force.some of them are: 1. Is it the Lorentz force that is actually responsible for the phenomenon of electromagnetic...
27. ### Uncharged particle in a magnetic field suddenly gets charged

What happens to the velocity? Say we have a piece of space debris in free fall. It has a particular velocity at a given time. Then say at some later time it's bombarded with ionic gas or something that causes it to become charged. Does the velocity change? My guess would be yes, because the...
28. ### Confusion about the Lorentz force

We can find the force by finding the E-field on the charge first, then applying Lorentz force formula. However, it isn't obvious to me at all how to find the E-field. If the charge were on top of the hemisphere I would be using spherical coordinates, but here I don't know which coordinate system...
29. ### Python Verlet algorithm and Lorentz force trajectory

I need to write a code to calculate the trajectory of the particle under lorentz force.Since the position depended equations are hard to solve I ll use a code, how can I appraoch this problem. I should use veloctiy-verlet algorithm or any suggestions ? You should consider that lorentz force is a...
30. ### Lorentz Force- Diff Eqn Solution

Homework Statement Solve the Lorentz Force Equation (Find ##\vec{r}(t)##) under constant ##\vec {B}## and ##\vec {E}##. İnitial Velocity: ##\vec{v_i}=<0,0,0>## İnitial position: ##\vec{r_i}=<0,0,0>## (##\vec {B}## and ##\vec {E}## are given values) Homework Equations Lorentz Force: ##\vec...
31. ### Lorentz transformation and Lorentz force

Lorentz transformation of electromagnetic field gives the relation ##E'=\gamma(E+v\times B)##. Lorentz force per unit charge is given as ##F=E+v\times B## without ##\gamma##. Don't we need coefficient ##\gamma## for F?
32. ### Lorentz force and linear motors

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38. ### Lorentz force - particle in an odd magnetic field

Homework Statement Particles of mass ##m## and charge ##q## are initially traveling in a beam along the ##z## direction with speed ##v## when they enter a long magnetic quadrupole lens, where there is no E-ﬁeld and the magnetic ﬂux density is ##B = Ay\hat{i} + Ax\hat{j}##, and where A is a...
39. ### Does the Lorentz Force Affect Both the Wire and Loop in a Current Loop Setup?

A current loop has a wire starting at its center. The wire terminates at the inside of the loop. The loop and wire have 150 and 15 ohms of resistance respectively. Both have 4 volts of potential across them. Looking at this I understand the the wire will experience a lorentz force because the...
40. ### Lorentz force on a charge due to a moving magnet

Let's say I have a charge q which is viewed from its rest frame. So it's velocity v is 0. So the so-called magnetic component of its Lorentz force, which is q v x B, is 0. But I can have a magnet moving in this frame of reference. Let's say the velocity of this magnet according to the charge's...
41. ### Proving that torque is m X B

Homework Statement Starting from the Lorentz force law, in the form of Fmag = ∫ I (d× B), show that the torque on any steady current distribution (not just a square loop) in a uniform field B is m × B. Homework Equations I looked at the solution I found in this thread here, but I don't...
42. ### Derivation of rate of energy change from Lorentz force

I am trying to derive from the Lorentz force equation the time derivative of the total energy. This involves using the equation for the jth electron in an electron beam traveling through an undulator. I have done it in such a way using the work done relation however I have been told that it is...
43. ### Ansoft Maxwell virtual vs Lorentz force

Hello people, I am trying to model a motor in maxwell that has an array of magnets in it , the thing is that I get the non zero forces for the magnets even when there are no excitations if I choose virtual forces , I am selecting the whole array of magnets so the computation should be for the...
44. ### Magnetostatics force equation for continuous current density

In Jackson, the following equations for the vector potential, magnetostatic force and torque are derived##\mathbf{m} = \frac{1}{{2}} \int \mathbf{x}' \times \mathbf{J}(\mathbf{x}') d^3 x'## ##\mathbf{A} = \frac{\mu_0}{4\pi} \frac{\mathbf{m} \times \mathbf{x}}{\left\lvert {\mathbf{x}}...
45. ### Problem with induction, Lorentz force and battery power

Homework Statement Hi everybody! I am struggling with an old exam problem, could someone maybe help me out to figure it out? Here is how it goes: A rod with resistance ##R = 0.1 \Omega## lays over two parallel tracks (resistance ##\approx 0 \Omega##, ##l=10##cm). A battery is connected...
46. ### Lorentz Force Law - Tensorial Form

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47. ### Few questions about Lorentz force

I have some confusion about the Lorentz force. First of all, I found that there are two equations for the Lorentz force: one of them is F = qE + qv × B , and the other one is just F = qv × B . What's the difference between them and how do you know which one to use? My other question is: Is the...
48. ### Which Rule is Correct for Determining the Direction of Lorentz Force?

Generally we use the left hand rule - (if index finger shows velocity, middle finger shows magnetic field, the thumb points towards force). Recently I also came across a left hand rule for lorentz force- Using your right-hand: point your index finger in the direction of the charge's velocity, v...
49. ### B An equation from terms of operator del to terms of sums

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50. ### Magnetic Force that Makes a Solenoid Valve Work

Hi guys, I am having quite the struggle finding a good resource to explain the difference between the magnetic force associated with moving charged particles (Lorentz Force) and just the regular force exerted by a magnetic field on a magnet or ferromagnetic material. I am trying to apply this...