Magnetic force on a charged particle

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Discussion Overview

The discussion revolves around the behavior of a positively charged particle moving through a magnetic field, particularly focusing on why the speed of the particle remains constant despite the presence of a magnetic force acting on it. The scope includes theoretical explanations and mathematical reasoning related to the effects of magnetic forces on charged particles.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions why the speed of the charged particle does not change when moving in a magnetic field, suggesting that the magnetic force is perpendicular to both the magnetic field and the velocity.
  • Another participant asserts that while the vector of speed changes direction, its absolute value remains constant due to the perpendicular nature of the magnetic force, although they also mention that the particle may lose kinetic energy through radiation.
  • Several participants request a mathematical explanation for the constancy of speed, emphasizing that when force is perpendicular to motion, no work is done, and thus kinetic energy remains unchanged.
  • It is noted that because the magnetic force does no work on the particle, it cannot gain or lose kinetic energy, leading to the conclusion that the speed does not change.

Areas of Agreement / Disagreement

Participants generally agree on the principle that the speed of the charged particle does not change due to the perpendicular nature of the magnetic force. However, there is a disagreement regarding the potential for the particle to lose kinetic energy through radiation.

Contextual Notes

The discussion includes assumptions about the definitions of work and kinetic energy, and the implications of radiation loss are not fully explored or resolved.

roshan2004
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I am considering a positive charged particle moving with the velocity v into the magnetic field field B making an angle theta with the magnetic field, so the magnetic force exerted on the charged particle is perpendicular to the plane of B and v. My question is-Why the speed of the charged particle doesnot change? Can you illustrate? And does it means that the velocity of the charged particle also doesnot change?
 
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roshan2004 said:
magnetic force exerted on the charged particle is perpendicular to [...] v. Why the speed of the charged particle doesnot change?
The vector of speed changes. Rotates. Its absolute value - remains constant. You answered yourself: because the force is perpendicular to the motion.

Actually, the particle will slow down, as it emits some of its original kinetic energy as a radiation.
 
can u tell me Mathematically why the speed doesnot change because of the fact that force is perpendicular to the motion?
 
Because the magnetic force is always at right angles to the velocity, no work is ever done by the force acting on the particle. [If you don't follow, look up the definition of work.] Because no work is done on it, the particle can't gain (or lose) kinetic energy from the force, so its speed doesn't change.
 
roshan2004 said:
can u tell me Mathematically why the speed doesnot change because of the fact that force is perpendicular to the motion?

When force is perpendicular to trajectory, there is no work done. So kinetic energy cannot change. So speed doesn't change.
 

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