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

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Discussion Overview

The discussion revolves around the Lorentz force and its implications for work done on a charged particle moving in a magnetic field. Participants explore the relationship between force, work, and energy transfer, particularly questioning why work is considered zero despite the presence of a force.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant states the Lorentz force is given by F = q (v х B) and questions why work done (W) is zero when the force is perpendicular to the displacement.
  • Another participant suggests that work is only done when the force has a component in the direction of the velocity.
  • A different participant challenges the notion that zero work implies zero energy, providing a counter-example of a particle moving on a frictionless surface.
  • There is a question about how a charged particle can maintain velocity in a magnetic field if no work is done, with a suggestion that the particle may have had initial energy before entering the field.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between work, energy, and motion in a magnetic field. There is no consensus on whether work should be considered done in this context, and the discussion remains unresolved.

Contextual Notes

Participants reference specific conditions under which work is calculated, such as the angle between force and displacement, and the implications of energy conservation in different scenarios. There are unresolved assumptions regarding the initial conditions of the charged particle.

spidey
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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?
 
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Do you think work should be done? Work is done where the force has a component in the direction of the velocity.
 
Phrak said:
Do you think work should be done? Work is done where the force has a component in the direction of the velocity.

if w=0 then energy =0, then how the charge q goes at velocity v in field B.from where the charge q gets energy?
 
spidey said:
if w=0 then energy =0
Not true. Counter-example: a particle sliding across a frictionless table with velocity v. There is no work being done, but then energy is non-zero.
spidey said:
then how the charge q goes at velocity v in field B.from where the charge q gets energy?
Perhaps, the charge was traveling at velocity v before it entered the magnetic field?
 

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