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Question
Write the expression for the Lorentz force on a particle of charge q moving with a velocity `vecv` in a magnetic field `vecB`. When is the magnitude of this force maximum? Show that no work is done by this force on the particle during its motion from point `vecr_1` to point `vecr_2`.
Solution
Lorentz force = Magnetic force + Electric force
⇒ `vecF = q(vecv xx vecB)`
`vecF = q.v.B sintheta`
when θ = 90° the Lorentz force is maximum.
If `vec(ds)` is the instantaneous displacement of charge and `vec(ds)` is also perpendicular to `vecF`.
Then,
W = `vecF. vec(ds)`
= `vecF vecs costheta`
= F.s cos90°
cos90° = 0
So, W = 0
Hence, no work is done by this force on the particle during its motion from a point `vecr_1` to point `vecr_2`.
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