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?

Question

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?

anonymous · Answer

The magnet force is always at right angles to the velocity, so it can do no work (work depends on the amount of the force in the direction of the displacement). If it can do no work, it cannot change the speed (work-kinetic energy theorem or conservation of energy) but of course it can change the direction of the velocity vector... therefore the velocity does change

anonymous · Answer

Thanks, How stupid I am to forget that!