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`.

Answer 1

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`.