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. P

    Lorentz force -> Current in a gradient field

    This is doing my nut in. I'm looking at causes of errors in a rotating gradiometer. It uses a loop of superconductor formed so that the current in the loop is proportional to the gradient of the magnetic field threading the loop. I think that an error current will arise due to the Lorentz...
  2. Peeter

    Q on Jackson. Lorentz force modification for radiation?

    Reading Jackson this morning, where it was stated that the Lorentz force equations: \frac{dU^\alpha}{d\tau} = \frac{e}{mc} F^{\alpha\beta} U_\beta are sufficient to describe the motion of a charged particle in an external field, neglecting the effects of radiation. That radiation...
  3. Somefantastik

    Lorentz Force Equation: Geometric Interpretation

    \textbf{L} \ = \ q\left( \textbf{v \ x \ B} \right) L, v, and B are vectors, and B represents magnetic induction. if \textbf{v} \ = \widehat{x}, then \textbf{v x B} = \widehat{x} \ \textbf{x B} What is this quantity, \widehat{x} \ \textbf{x B}, geometrically?
  4. S

    Lorentz force and Maxwell Equations

    I am trying to bridge a gap between Maxwell equations and Lorentz force. I know that they are not independent and in theory, one could be derived from the other but I cannot see that. More physics oriented people prefer the Lorentz force because it describes the effect of B and E as a final...
  5. N

    Troubleshooting a Homemade Rail Gun: Tips from an AP Physics Final Project

    For my Final Project for my AP Physics class is a rail gun. But I am having trouble getting it to fire anything or even move it. I have no trouble charging the bank but when it is discharged into the rails the projectile doesn't move. I am using 11, 330v disposable camera capacitors in...
  6. D

    Newton's 2nd law and Lorentz Force

    ok, the lorentz force equation is F=q(E+v x B) and Newton's 2nd law is F=ma. I need to combine the two to show that ma.v=qE.V I don't really know what to do first here... i can see the simple substitution so that ma=qE+q(v x B) but beyond that...do u change the a to dv/dt. Any type of help...
  7. Q

    Lorentz force on current-carrying wire

    Homework Statement Given: a quarter-circle of wire (radius r=0.75m) in a uniform 1.7T magnetic field carrying a current of 3.5A (see diagram) Find: The force on the wire. Note: the connecting wires delivering the current to the quarter circle are parallel to the magnetic field and...
  8. S

    Lorentz Force and Coulomb Force

    Homework Statement In frame S, two identical point charges q move abreast along lines parallel to the x-axis, a distance r apart and with speed v. Determine the force in S that each exerts on the other: a) using the lorentz force in conjunction with the field of a moving charged particle...
  9. X

    Reconciling Magnetism in material and the Lorentz Force equation

    Hello, The Lorentz force equation, F = q (E + v x B), is a complete description of the force on bodies arising from Magnetism and Electricity, right? So somehow it must be possible to get from the magnetism that exists in materials (like in a magnet) to this equation. I don't see how the...
  10. C

    Lorentz Force Law to determine the magnitude and direction of an electric field

    Homework Statement Ok here it goes... A stream of electrons, each with speed u = 5.9 x 10^6 m s^-1 and traveling along the x-axis in the positive x-direction enters a region pervaded by a uniform magnitic field B. The electrons the describe a circle with raidus R in the horizontal xy-plane...
  11. X

    Magnetic Fields and Lorentz force flaw

    HI all: I have one confused question. a infinitely long wire carrying constant direct current is placed in the space. One particle with charge q and velocity v is moving in the magnetic field which is created by current-carrying wire. We know in the lab frame. particle will accelerate in this...
  12. M

    Lorentz force: absolute reference frame?

    F= q(v x B) B= v x q*k*d/r^2 It is a basic physics knowledge magnetic field forms around moving charge, it tell us magnetic field is zero when charge is not moving and strength of magnetic field increases as velocity increases, right? Magnetic potential vector field increases with "absolute...
  13. N

    Is the Lorentz force quantized at the atomic level?

    Does the lorentz force occur at the atomic level?
  14. S

    How Many Teslas Are Needed to Deflect Cosmic Rays at Near Light Speed?

    I am trying to calculate the strength of the magnetic field ( in teslas ) that would be needed to deflect cosmic rays going about 99% the speed of light. using the lorents force http://en.wikipedia.org/wiki/Lorentz_force I replaced force with mass times acceleration I canceled...
  15. Hans de Vries

    The Lorentz force derived from the Klein Gordon equation

    The Lorentz Force and Maxwell's equations derived from Klein Gordon's equation . http://www.physics-quest.org/Book_Lorentz_force_from_Klein_Gordon.pdfI posted several new chapters of my book lately, mostly involving the Klein Gordon equation. This chapter shows how the Lorentz Force has a...
  16. KleZMeR

    DSolve; Lorentz Force equations of motion

    Hi, I am trying to use DSolve in Mathematica 6.0.1.0, in order to find equations of motion (x[t], y[t]) from second-order differential equations. I have looked through much documentation, and attempted numerous codes to figure this out, but get many errors or the same answer every time. This...
  17. S

    How Does Lorentz Force Affect Work Done Despite No Energy Transfer?

    From Lorentz force law, F = q (v х B) = q v B sin θ F = q v B [For θ = 90] W = F * d = F d cos θ w = 0 [For θ = 90] How come we have a force but no work done?
  18. Peeter

    Covariant form of the Lagrangian for Lorentz force.

    If I use the following Lagrangian: \mathcal{L} = \frac{1}{2} m v^2 + e A \cdot v/c = \frac{1}{2} m \dot{x}_\mu \dot{x}^\mu + e A_\nu \dot{x}^\nu /c I can arrive at the Lorentz force equation in tensor form: m \ddot{x}_\mu &= (q/c) F_{\mu\beta} \dot{x}^\beta details offline...
  19. Peeter

    Application of Noethers to Lorentz force Lagrangian with boost

    I've been slowly self studying Lagrangian topics, and have gotten to Noether's theorem. I've tried application of a Lorentz boost to all the terms in the Lorentz force Lagrangian (which is invariant with respect to boost since it has only four vector dot products). Then using Noether's...
  20. Peeter

    Derivation of Lorentz force Law strictly from maxwell's equations?

    Basic electrostatics (as I've seen it presented) usually starts off with an implicit \mathbf{F} = q q_2 \hat{\mathbf{r}}/r^2 = q \mathbf{E} definition of the electric field. Then with a limiting volume argument, you can then show that this can be expressed div \mathbf{E} = \rho. Eventually one...
  21. V

    Relativistic Application of the Lorentz Force

    Hi! I would really appreciate some help on the relativistic Lorentz force as applied to a charged particle; it's my first post on this site btw. Thanks in advance ;) QUESTIONS (a) A charged particle with total energy E0 is injected into a region of space containing a uniform...
  22. M

    Relativistically correct exression for Lorentz force

    I need to know the correct expression for the Lorentz force on a relativistic particle in an EM field, in cgs units, in terms of vector potential A and scalar potential phi, to prove that a given Lagrangian produces the correct equations of motion. I don't need it in covariant form with tensors...
  23. T

    Lorentz force in superconductors

    Hi, everyone. In a course on superconducting materials, my lecturer has suggested that in a Type I(one) superconductor, any normalconducting region containing trapped magnetic flux will feel a Lorentz force per unit volume F_L = J \times B, where J is the transport current density (vector!)...
  24. B

    A system of differential equations - Lorentz Force

    I was wonder if anybody might know how to solve this (this is not a homework problem, btw). The Lorentz Force is given by: \vec{F}=q(\vec{E}+\vec{v}\times\vec{B}) Now afer working that out, I get three differential equations: \frac{dv_x}{dt}=\frac{q}{m}(E_x+v_yB_z-v_zB_y)...
  25. D

    Calculating Electric Field Using Lorentz Force Law

    [SOLVED] Lorentz Force Law Problem Problem and known data: 34.6 An electron travels with velocity 4.9 X 10^6 m/s in the i direction, through a point in space where the magnetic field is .111 T in the j direction. The force on the electron at this point is F=(9.5 x 10^-14 i - 9.5 x 10^-14...
  26. E

    Understanding the Lorentz Force

    [SOLVED] lorentz force Homework Statement Say you a magnetic field perpendicular to the direction of a current. If you consider the current as electrons moving forward then the Lorentz force on the electrons points up (say). But if you consider the current is a lot of positive charge...
  27. B

    Why does Lorentz Force law work?

    Why does it, and these other laws/effects work? Can anyone explain why the Right Hand Rule works, on a quantum scale? Lorentz Force law http://www.ee.byu.edu/em/lorentz.htm Right hand rule http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html The hall effect...
  28. G

    Using Right Hand Rule & Lorentz Force Law to Find Electric Field Direction

    I have a question regarding electrons in an electric and magnetic field and I need to apply Lorentz force law to find the direction in which the electric field is pointing. Would someone be good enough to explain how the right hand rule applies in this situation? I think I might be getting...
  29. D

    Relativity - Lorentz Force Law

    Assuming the Lorentz force law and also that in the rest frame of the particle the 3 acceleration is zero, we need to explain why the following equations hold: E.v = 0 and E + v.B = 0 where v is the velocity. I think this is because g(A,A) = -a squared is invariant. Therefore if a=0, I...
  30. M

    Lorentz force law and capacitor problem

    An electron is moving with a speed of V when it enters an electric field generated by two equally but oppositely charged parallel plates. The electron passes through the field without being deflected. How can this be? I was thinking that the electrons electric field would cancel out with...
  31. I

    Lorentz Force Part 2: Proving v.E = 0, E.B = 0, v ≥ E/B

    Homework Statement The motion of a charged particle P, observed in an inertial frame S. It is found that P moves with constant velocity v through a region of space where there is a uniform electric field E and a uniform magnetic field B. The speed v = |v|and the field magnitudes E = |E| and...
  32. I

    E = F/q - (V*B)Lorentz Force Law Part 1: Finding E

    Homework Statement The motion of a charged particle P, observed in an inertial frame S. It is found that P moves with constant velocity v through a region of space where there is a uniform electric field E and a uniform magnetic field B. The speed v = |v|and the field magnitudes E = |E| and...
  33. J

    Understanding Lorentz Force and Its Applications

    Was wondering if anyone is familiar with lorenzt force? Here is the problems whatever help you can give that would be great thank you in advance. Does anyone know a good site to practice these types of problems Homework Statement An electron is moving initially in the +x direction in a...
  34. A

    Electromagnetism - Lorentz Force

    Homework Statement A particle of charge q starts from rest at the origin of coordinates in a region where there is a uniform electric field of strenth E parallel to the x-axis, and a uniform magnetic field B parallel to the z-axis. Find the equations of motion, and solve them to show that...
  35. E

    Lorentz Force Law derivation using the Lagrangian

    * implies time derivative, _i and _j are indices. Homework Statement Consider a Particle of mass m and charge q acted on by electric and magnetic fields E(x,t) and B(x,t). these fields can be described in therms of the scalar and vector potentials PHI(x,t) and A(x,t) for which E= -...
  36. A

    Can Lorentz Transformation Explain Magnetism and the Lorentz Force?

    I read somewhere that the whole of magnetism, and in particular the lorentz force, can be found merely by applying the lorentz transformation to transform the coordinates of the electric field of a charged particle from the frame in which the particle is at rest to a frame in which the particle...
  37. A

    Force as a Function of Velocity (Lorentz Force)

    A singly charged lithium ion is accelerated by an electric field E=10i V/m applied between two plates ten centimeters apart. After passing through a small hole in the negative plate, the ion enters a region of space where there is a magnetic field B=5j mT. The ion moves in a circular path. What...
  38. G

    Is Lorentz Force Truly Conservative?

    \mathbf \nabla \times (\mathbf E + \mathbf v \times \mathbf B) pluggin stuff from Maxwell equations = -\frac{\partial B}{\partial t} + \mathbf v (\mathbf \nabla \cdot B) - \mathbf B (\mathbf \nabla \cdot v) Since \frac{\partial}{\partial t}(\mathbf \nabla \cdot \mathbf r) = 0 it's =...
  39. B

    In a railgun the lorentz force causes an object to be propelled

    In a railgun the lorentz force causes an object to be propelled in a direction because of an electromagnetic force caused by running a current through the "rails". How come you can use aluminium or another such non-magnetic metal as both rails and armature? Surely only a magentic metal would work?
  40. W

    Calculating the Lorentz Force of an Electron in Magnetic Field

    A diagram I attached (you can view the website) shows a uniform magnetic field of magnetic flux density B[Wb/m^2] parallel to the x-axis. On the xy-plane, an electron of electric charge -e[C] and mass m[kg] departed from the x-axis in the direction of \theta[rad] with a speed of v[m/s]. Then the...
  41. S

    Understanding Lorentz Force: Accelerating a Wire

    I'm having difficulty with this whole concept I understand that the Lorentz force is the force acting on a charged particle in a magnetic field, and that it is the resultant of the forces due to the electic field and the magnetic field. The situation which I am applying this to is a...
  42. E

    How Does the Lorentz Force Fit into Classical Electromagnetism?

    I thought in classical physics, only four forces account for all mechanics: 1 gravitational attraction 2 electromagnetic force 3 nuclear strong force 4 nuclear weak force There is also a Lorentz force on a charged particle moving through a magnetic field. How does classical EM...
  43. M

    Lorentz Force Law, am i messing up vector algebra?

    Okay here is my work: http://show.imagehosting.us/show/891312/0/nouser_891/T0_-1_891312.jpg and here is my calculations part: http://img136.imageshack.us/img136/5539/lastscan7qc.jpg Problem says: 14. [HRW7 28.P.008.] An electron has an initial velocity of (14.0 j + 21.0 k) km/s and a...
  44. M

    Lorentz Force Equation – Is vxB Representable?

    Hi All, Just a thought. The Lorentz force equation as we all know is: F = qE + qvxB. We know that Electrical Field can be written as del(Phi), where Phi is the electrical potential. Also, Force can be written as del(Energy) - correct me on this one. Hence is there a representative term...
  45. M

    Does Lorentz Force Change in Moving Frames?

    Consider a magnetic field with a charge at rest in inertial frame S. From this reference point the particle is not moving wrt the magnetic field and will not experience a Lorentz force. Now consider a frame S' moving wrt S at a constant speed. An observer in this frame would see the charge...
  46. I

    The Lorentz force in the MKS and CGS measurement systems

    Hi there! I have a problem deriving the formula for the Lorenz force that I found in my lecture notes in Theoretical Mechanics. The formula is: \vec{F}=q \cdot \vec{E} + \frac{q \cdot (\vec{v} \times \vec{B})}{c} Where: \vec{F} is the Lorentz force \vec{E} is the electric...
  47. F

    Lorentz Force Reaction: Exploring Newton's 3rd Law in Classical Demonstration

    In classical Lorentz force demonstration, let's say we have 2 permanent magnets generating a magnetic field perpendicular, out from the page and a wire carrying current to the left. Thus we would expect that the Lorentz Force will exert an upward force on the wire. According to Newton's 3rd...
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