Problem with use of 'velocity' of charged particle in lorentz force eq

In summary, the conversation discusses the effect of a uniform magnetic field on a charge particle and how it changes when observed from a different reference frame. The force on the particle due to the magnetic field will be less when observed from a moving reference frame, as calculated by the Lorentz force equation. The question arises about the right solution for this scenario, specifically regarding the assumption of a fixed magnetic field in relation to both frames of reference. It is noted that a Lorentz transformation of the magnetic field will produce an additional E field.
  • #1
pratikaman
8
0
if we assume a charge particle enters in a uniform magnetic field with velocity V w.r.t inertial frame as shown fig. then according to the situation shown there will be force acting on particle due to magnetic field (neglecting B field induced due to charged particle itself). But now if we observe this situation from a frame of reference which is moving with velocity V' in direction of particle's velocity with respect to inertial frame then velocity of particle observed in that frame will be V-V'. then force on particle due to magnetic field will be less (As calculated by lorentz force equation) than as calculated in inetial frame.

what will be the right solution for this case?
 

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  • #2
Are you implying/specifying/assuming that the magnetic field is fixed in relation to both reference frames?
 
  • #3
There will now be an E field, becuse a Lorentz transformation of B produces an E field.
 

1. What is the Lorentz force equation?

The Lorentz force equation is a fundamental equation in electromagnetism that describes the force exerted on a charged particle by an electric and magnetic field. It is given by F = q(E + v x B), where F is the force, q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field.

2. Why is there a problem with using velocity in the Lorentz force equation?

The problem with using velocity in the Lorentz force equation is that it does not take into account relativistic effects. At high velocities, the velocity term in the equation becomes significant and can lead to inaccurate results. This is because the equation was derived from classical mechanics, which does not consider the effects of special relativity.

3. How does special relativity affect the use of velocity in the Lorentz force equation?

Special relativity states that as an object approaches the speed of light, its mass increases and time dilates. This means that at high velocities, the velocity term in the Lorentz force equation becomes increasingly inaccurate. Additionally, the equation does not account for the change in momentum due to the increase in mass at high velocities.

4. Is there a solution to the problem with using velocity in the Lorentz force equation?

Yes, there is a solution to this problem. The Lorentz force equation can be modified to include relativistic effects by using the relativistic momentum instead of velocity. This modified equation is known as the relativistic Lorentz force equation and is given by F = q(E + p x B), where p is the relativistic momentum. This equation is more accurate at high velocities and takes into account the effects of special relativity.

5. How does the problem with velocity in the Lorentz force equation impact scientific research?

The problem with using velocity in the Lorentz force equation can lead to inaccurate results and can affect scientific research in areas such as particle physics and astrophysics. It is important for scientists to use the correct equations and take into account relativistic effects in their research to ensure accurate and reliable results.

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