Magnetic force on a charged particle

[roshan2004]

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?

 

[xts]

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.

 

[roshan2004]

can u tell me Mathematically why the speed doesnot change because of the fact that force is perpendicular to the motion?

 

[Philip Wood]

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.

 

[mathfeel]

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.