A charged particle with mass m and electric charge q is morn

A charged particle with mass m and electric charge q is morning in a constant magnetic field B. It experiences the Lorentz force F = 9 V times B, where V is the particle velocity. According to the 2^nd Newton\'s law, the particle\'s acceleration is a = q/m v times B Show that the speed of the particle, v = ||v||, does not change.

Solution

As you have mentioned Force on the charge due to magnetic field is F_B = q(v x B).
Hence acceleration provided by Lorentz force F_B , a = (q/m)(v x B).
The cross product reminds us that velocity and acceleration are in perpendicular directions. Therefore, no component of acceleration will be in the direction of velocity. Implies, acceleration can\'t change the velocity, only its direction can change.
Also you have mentioned Speed ||v|| , which is equal to v.v (dot product of velocity) will not change because no change in velocity.