Lorentz force Definition and 202 Threads

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. Dewgale

    Is the Lorentz Force Law Consistent with \( P^\mu P_\mu = -m^2 \)?

    Homework Statement Show that the Lorentz Force Law, \frac{dp^{\nu}}{d \tau} = -q U_{\mu} F^{\mu \nu}, is consistent with P^\mu P_\mu= -m^2. Here U is the 4-velocity, F is the Electromagnetic Tensor, and p is the 4-momentum. (Minkowski Space) Homework Equations As stated above. The Attempt at...
  2. A

    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...
  3. P

    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...
  4. olgerm

    B An equation from terms of operator del to terms of sums

    https://wikimedia.org/api/rest_v1/media/math/render/svg/a7fd3adddbdfb95797d11ef6167ecda4efe3e0b9 https://en.wikipedia.org/wiki/Lorentz_force#Lorentz_force_in_terms_of_potentials How to write this formula in terms of sums and vector components? What is ##v\cdot\nabla## ? I think it is some...
  5. AvroArrow

    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...
  6. peasqueeze

    I Use Lorentz Force to Find Magnetic Field Components

    So I am constructing an analogy between the self replicating fracturing effect on thin films and the path of a charged particle. (Qualitatively, several cracks have similar shapes to charged particle motion) I won't go into the details of the fracture mechanics, so I will only use E+M...
  7. Delta2

    Do Moving Charges Create Magnetic Fields, or is it Something Else?

    Ok so when we have a current carrying conductor inside a magnetic field there would be Laplace force ##L\times Bi## which is the macroscopic form of the microscopic Lorentz force ##v\times Bq## in a large number of electrons ( or it is not ?) But also there will be hall voltage which will...
  8. Quadrat

    Electron passing through a magnetic and an electric field

    Homework Statement An electron with velocity ##\vec{v}_0=8.7*10^4(m/s)## (in the î direction) passing through an area with a uniform magnetic field ##\vec{B}=0.80 T## (in the negative k̂ direction). There's also a uniform electric field in this area. What is the magnitude and direction of...
  9. A

    Electron enters magnetic field at 5000V -- What's the radius?

    Hi! I'm getting ready for an exam and want to make sure if I solved some problems correctly. I would be grateful for your feedback :smile: 1. Homework Statement After going through potential difference of 5000 V an electron falls in uniform magnetic field. It’s induction is 0.1T and the...
  10. S

    Lorentz Force Law Homework: Proton & Negative Stream

    Homework Statement A relativistic proton is traveling next to a stream of negatively charged particles that are traveling at the same velocity as the proton. I'm to find the force on the proton by transforming the field from the negative stream to a stationary lab frame. Homework Equations f=...
  11. S

    Calculate pressure difference in current-carrying mercury

    Homework Statement A vertical column of mercury, of cross-sectional area A, is contained in an insulating cylinder and carries a current I0, with uniform current density. By considering the column to be a series of concentric current carrying cylin- ders, derive an expression for the...
  12. T

    I A special relativity explanation for the Lorentz Force?

    I am still a bit puzzled by this video: Does this mean that force exerted on an electrically charged particle facilitated by moving through magnetic field B is due to special relativity, and not virtual photons acting as magnetic force carriers? Thanks
  13. S

    Ions & Lorentz Force: Collisions w/ Oppositely Charged Electrodes

    When ions collide with oppositely charged electrodes, do they experience a Lorentz force as they gain or lose electrons? Is there a force, ignoring the repulsion of the positive electrode, in the direction of the blue arrow depicted here? Only information I find is on ionic fluids.
  14. M

    Why does Lorentz force have that particular direction?

    Why does Lorentz force have that particular direction? Why is it perpendicular to the magnetic intesity and the current? Is it cause of some photons' reactions? Thanks
  15. J

    Dual Lorentz force for classical spin-orbit interaction?

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  16. M

    Relativistic Transformation of Lorentz Force (E + v x B)

    Here is a problem: Imagine two equally charged capacitor plates parallel to the x-y axis, whose area is large enough compared to the distance between them that fringe effects can be ignored. The bottom plate (at z=0) is + charged, and the top is - charged. The vector field E is therefore...
  17. densaface

    Why is the Lorentz force calculated in Ansys Maxwell so low?

    Why is the Lorentz force calculated in Ansys so low? According to the formula F=B*I*l, it is supposed to be at least 1000 times higher. The model is really simple: a magnetically conductive plate in a static magnetic field inducts the magnetic field from the surrounding space, which makes its...
  18. rogerk8

    Cross product evaluation (for the Lorentz Force).

    Let's say we have: \vec{E}=E_x\vec{i}_x+E_y\vec{i}_y+E_z\vec{i}_z and \vec{B}=B_x\vec{i}_x+B_y\vec{i}_y+B_z\vec{i}_z and the Lorentz Force 0=q(\vec{E}+\vec{v}X\vec{B}) which due to \vec{E}X\vec{B}=\vec{B}X(\vec{v}X\vec{B})=vB^2-B(\vec{v}\cdot \vec{B}) and transverse components only...
  19. A

    Lorentz force in different frames of reference

    Hi, I have been studying lorentz force . The book says force experienced by a charge in magnetic field is But velocity is a relative concept . In one frame of reference(inertial frame) I might observe the charge moving with some velocity and in the 2nd frame(inertial too) I might observe the...
  20. cnh1995

    Motoring Effect in DC Motors: Magnetic Field Interaction or Lorentz Force?

    When current flows through the armature winding of a dc motor, what exactly happens in there that produces the torque? Is there a force due to the interaction between two magnetic fields or Lorentz force acts on the conductor electrons? Basically, why does motoring effect take place? Is it due...
  21. A

    Lorentz force in motor other than homopolar

    Hello, I am trying to build a motor. Just a prototype I guess and learning at the moment so just simple stuff but I can't make it work.. I have seen the examples of a homopolar motor and understand the direction of force due to Lorentz force. To be simple I don't want, and don't see the need...
  22. A

    Velocity frame of reference in lorentz force equation

    Hi, I am new here, but there is a question that really bugs me :-(. In Lorentz force why was the velocity defined as relative to the observer and not relative to thesystem generating the magnetic field. By defining it relativ eto the system relativity is not needed to explain how an observer...
  23. PhiowPhi

    Lorentz force system, what to expect?

    I'm building a system that is using the Lorentz force principle, of when a wire is placed in a magnetic field(##B##) with length(##L##) and has current flowing(##I##) there is a force = ##IL \times B## that would move the wire. I want to take into account of every single thing that will happen...
  24. E

    Lorentz Force & Newton's 3rd Law

    Hello, I have been wondering this for a while and have only recently thought to ask here. The Lorentz force is the interaction of a moving charge in a magnetic field, it doesn't seem to have any sort of physical force applied to it, only the magnetic interaction. I was wondering, if there is...
  25. S

    Physics question from my test, having a hard time solving it (Lorentz Force)

    Homework Statement http://www.solutioninn.com/physics/electricity-and-magnetism/magnetic-fields/particle-with-charge-2.15uc-and-mass-3.20-x-10-11-kg-is I am just going to link this because I don't know how to draw a nice diagram like that and put it here. But essentially that is the question...
  26. D

    Finding Magnetic Field using Lorentz Force

    Homework Statement Show that two measurements F1 and F2 of magnetic force at a fixed point are sufficient enough to determine B at that point as (see picture) provided v1 and v2 are orthogonal. 2. Homework Equations F = qv x B Bz = cFx/(qvy) By = cFz/(qvx) Bx = cFy/(qvz) The Attempt at a...
  27. PhiowPhi

    Net Lorentz force, of a non-linear wire.

    From the diagram above, there are two types of wires a straight wire and a non-straight wire(zig-zag shaped wire), that are both placed inside a magnetic field(B), and have current flowing in both of them as well. The straight wire will experience a force and will move towards the left as...
  28. Coffee_

    Can the Lorentz force explain the following phenomenon?

    The situation is probably well known by many of you. The setup is at rest realtive to the B-field while the rod is moving at a constant velocity. I have been thinking about the connection between the Lorentz force and Maxwell 3 and looking stuff up about it. The first question is wheither only...
  29. PhiowPhi

    Induced-EMF and the Lorentz force?

    When a wire( that has the flow of I) is placed inside a magnetic field(B) experiences the Lorentz force and beings to accelerate in the uniform and constant magnetic field, there is no induced EMF correct? Only when it starts to exist the magnetic field there is change in flux. And there is...
  30. V

    Using Lorentz Force Equation to find kinetic energy of a particle.

    Homework Statement A charged particle (m=1.673*10^-27 kg) exists in a region with E=10 kV/m in the x direction and B=1T in the y direction. If the particle moves without being deflected calculate its kinetic energy. Homework Equations F=Q(E+u x B) and KE=1/2 mu^2 where u is velocity. This is...
  31. T

    About Lorentz force and Lenz' law

    Hello Physics forum, I have come here seeking for some experienced help about a doubt that to some extent is not letting me advance on my studies of electromagnetism. Basically is about the magnetic (B) field, and more specifically, about the force at each point of the vector field (The lorentz...
  32. P

    Lorentz force and work done: where is the glitch?

    Where is the glitch? 1. Let a single free electron move along x-axis with constant speed Vx. It encounters magnetic field on its right side, so the Lorentz force accelerates it along y-axis and it gains speed Vy. --- Glitch or pass? 2. The electron does not slow down in x direction when...
  33. I

    Obtaining potential from Lorentz Force

    Two part inquiry PART I Situation: I have a B-field and I'm pulling a straight piece of wire through that B-field You pull the wire perpendicularly through the B-field at velocity v; charges between points a and b will experience the Lorentz Force and will begin to move along...
  34. E

    How can the Lorentz force law be derived using the action principle?

    Hi, I am trying to derive the Lorentz force law in the following form: q \frac{dw^\mu}{d\tau} = q w^\mu \partial_\nu A_\sigma \epsilon_\mu^{\nu \sigma} by varying the following Lagrangian for a classical particle: S = \int d^3 x \left( -m \int d\tau \delta(x-w(\tau) ) + q \int d\tau...
  35. D

    Work done by the Lorentz force?

    When a wire is placed in a magnetic field and current flows in that wire work is done on the wire and be calculated: 1) W = Fd 2) F = IL x B 3) W = ( IL x B )x d Must there be any derivations beyond what is above? If everything is "given" or... measured via instruments. Then...
  36. D

    Change in electrons direction, changes the Lorentz force direction?

    When the Lorentz force is applied on a wire that has current flowing in a magnetic field, by changing the direction of the electron(not it's KE) would this possibly change the direction of the Lorentz force? Can the wire be controlled in a way that the force's direction stays the same path?
  37. D

    Is the Lorentz force conservative?

    When a wire has current I in a magnetic field B, there is the Lorentz force is it considered a conservative force or not? Please do explain as to why it is.
  38. Entanglement

    Beyond Lorentz Force: Electron Circles in Magnetic Field?

    When a wire is placed in a magnetic field, Lorentz force acts on an electron in a direction perpendicular to velocity and to the magnetic field, since the magnetic force is perpendicular to the velocity the electron will only change direction with no velocity change, what happens after that, I...
  39. U

    EM Momentum,Hidden Momentum,Centre of Energy Theorem and Lorentz Force

    I recently read Griffiths paper on Hidden momentum, and still didn't found it complete. Following is the short summary. The usual setup of current carrying loop and a charge lying nearby, according to the paper, Shockley and James presented the problem, that is, when we let the current die...
  40. C

    Lorentz Force on a Curved Wire in a Non-Constant Magnetic Field

    What is the formula to evaluate Lorentz force on a curved current carrying wire in a non-constant magnetic field (given by some known vector field). The standard form of Lorentz force (Fb=BxlI) when B and the wire's length 'l' are constants does not account for this case, nor does the...
  41. A

    Calculation of Lorentz Force in Generator and its mass equivalence

    Greetings All - Per F=BIL I can calculate quantity of Force on coil (or magnet), when I draw certain amount of current from the generator. So I need help in calculating the Force and then weight equivalent of it. Let's say I have Single coil [with 300 turns] generator [wire length = 92...
  42. V

    Show equivalence of Force to Lorentz Force

    Greetings, I am trying to to show that the force in this form: \dot{P}=e(\vec{∇}\vec{A})\vec{\dot{x}}-e\vec{∇}\phi Is equal to the lorentz force. I have been trying the approach of some sort of vector identity but have not gotten anywhere. The equation and where I am trying to get...
  43. tom.stoer

    How Does the Lorentz Force Act on a Superconducting Ring in BCS Theory?

    BCS theory is able to derive the London equations and the Meißner-Ochsenfeld effect. Experimentally the Meißner-Ochsenfeld effect can be demonstrated via levitating superconducting rings. So we have the usual Lorentz force acting on the Cooper pairs carrying the current. However in order to...
  44. D

    How can we express the Lorentz force law in SI units?

    How do we say that F=BIL SINΘ using the SI units?:confused: Newton(N)= Weber/m2 * ampere*meter. please explain as soon as possible.:approve:
  45. E

    Lorentz Force and right hand rule

    Homework Statement > Figure 1: > > A spool is hung on a spring. A part of the coil hangs in front of a > homogeneous magnetic field. The coil is incorporated in an electrical > circuit. See Figure 1. > > the coil KLMN has a rectangle shape, has a height of 10.0 cm, a width > of 8.0 cm, and...
  46. L

    Lorentz force in a toroid coil

    Hi, I'm having a major issue trying to work out where the resultant lorentz force might act when I have a wire coiled around a doughnut (toroid) shape. Am I right in saying that there will be a resultant lorentz force acting to crush the doughnut because there will be a slightly denser...
  47. leviterande

    Lorentz force on a wire in earth´s Magnetic field?

    Hi all! First, this is neither a part of homework, university or anything like that , it is my own wondering. I have been searching a lot for how to calculate the Lorentz force acting on a single current carrying wire in Earth´s magnetic field which is 0.6 Gauss. for say a wire of voltage...
  48. E

    Questions regarding Lorentz force

    Why doesn't a stationary charge experience a magnetic force? And why does a moving charge produce a magnetic field? From a previous thread on the topic I understand it is from the relativistic interpretation of its electrostatic field. So then why shouldn't it affect a stationary charge?
  49. P

    Determine Magnetic Field from Lorentz Force

    Homework Statement From Zangwill, Chapter 2. Suppose that the instantaneous forces on a charge, q, when it is moving with velocities \vec{v}_1 or \vec{v}_2, are \vec{F}_1 and \vec{F}_2, respectively. Without choosing a coordinate system, show that \vec{B}(\vec{r}) can be determined by working...
  50. B

    How is Velocity Calculated in Lorentz Force Spectrometry?

    If a particle of mass m and charge q (where q can be negative or positive, and the velocity should be positive if q is positive and negative if q is negative) is passed through an electric field of potential Vd, what is the velocity v of the particle? Or possibly this should be a vector...
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