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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.
Solution
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.
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