Compute the work done and power delivered by the Lorentz force on the particle of charge q moving with velocity `vec(v)`. Calculate the angle between Lorentz force and velocity of the charged particle and also interpret the result.

Explanation

For a charged particle moving on a magnetic field. `vec(F) = q(vec(v) xx vec(B))`
the work done by the magnetic field is W = `int vec(F).d vec(r) = int vec(F).vec(v)`dt
W = q `int (vec(v) xx vec(B) ) .vec(v)`dt = 0
Since `vec(v ) xx vec(B)` is perpendicular to `vec(v)` and hence `(vec(v) xx vec(B)) . vec(v) = vec(0)` This means that Lorentz force do no work on the particle.
`(dW)/(dt) = P = 0 `
Since, `vec(F).vec(v) = 0 rArr vec(F) and vec(v)` are perpendicular to each other. the angle between Lorentz force and velocity of the charged prticle is `90^(@)`. thus lorentz force changes the direction of the velocity but not the magnitude of the velocity. hence Lorentz force does no work and also does not alter kinetic energy of the particle.