Question

State the expression for the Lorentz force on a charge due to an electric field as well as a magnetic field. Hence discuss the magnetic force on a charged particle which is (i) moving parallel to the magnetic field and (ii) stationary.

Answer 1

A charge q receives a magnetic force perpendicular to both `vecB` and `vecv` when travelling at a velocity of `vecv` through an induction magnetic field of `vecB`. According to experimental measurements, the force's amplitude is related to the particle's velocity, charge q, and the sine of the angle θ formed by `vecv` and `vecB`. That is the magnetic force's magnitude. `vecF_m = qvBsinθ`

∴ `vecF_m = q (vecv xx vecB)`

Both the electric and magnetic fields act on a charged particle as it travels through an area of space that is subject to both of them.

The force due to the electric field `vecE` is `vecF_e = q vecE`.

The Lorentz force is the overall force acting on a moving charge in an electric and magnetic field.

`vecF` = `vecF_e` + `vecF_m` = q `(vecE + vecv xx vecB)`

Special cases:

1. `vecv` is parallel or antiparallel to `vecB`: In this case, F_m = qvB sin 0° = 0. That is, the magnetic force on the charge is zero.
2. The charge is stationary (v = 0): In this case, even if q ≠ 0 and B ≠ 0, F_m = q(0)B sin θ = 0. That is, the magnetic force on a stationary charge is zero.