Question

why velocity of proton changes while it move freely in a magnetic feild but speed remain constant​

Answer 1

The magnetic force exerted will be perpendicular to the direction of motion of the proton. As we know when when force acting is perpendicular to the direction of moving charge, work done will be zero. It means kinetic energy does not change. The force is able to change the direction (velocity) of the proton but not its speed (magnitude). Thus momentum and velocity changes

Answer 2

Another way to look at this is that the magnetic force is always perpendicular to velocity, so that it does no work on the charged particle. The particle's kinetic energy and speed thus remain constant. ... The magnetic force is perpendicular to the velocity, so velocity changes in direction but not magnitude

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