Question

Write the expression for Lorentz magnetic force on a particle of charge ‘q’ moving with velocity `vecv` in a magnetic field`vecB`. Show that no work is done by this force on the charged particle.

Answer 1

 

Lorentz magnetic force,`vecF = q (vecV xx vecB)`

Work done due to Lorentz force

`W = vecF*vecr`

 = `q(vecV xx vecB)*vecr`

=`q[vecB * vecr - vecV*vecr]`

`q[0 -0] =0`

as `vecr ⊥ vecB and vecr ⊥vecv`

Hence, work done by the force on the charged particle will be zero.