Question

What is the direction of the magnetic force on the proton? What is the magnitude of the magnetic force on the proton?

A proton is traveling west, with speed 4 x 10^5 m/s. The proton encounters a magnetic field of 0.34 T going east, due to current running in a nearby wire.

Answer 1

Magnitude of the magnetic force on the proton is understood as magnitude of the force experienced by the proton in the magnetic field which has been calculated and is `=0`.

Explanation:

Force experienced by a charge particle having charge `q` when it moves with velocity `vecv` in an external electric field `vecE` and magnetic field `vecB` is described by the Lorentz Force equation:

`vecF= q(vecE+ vecv times vecB)`

Given a proton moving West encounters a magnetic field going to East. As there is no external electric field, above equation reduces to
`vecF= qcdot vecv times vecB`

As the velocity vector of proton and magnetic field vector are opposite to each other, angle `theta` between the two`=180^@`.
We know that `sin180^@=0`.
Consequently the cross product vanishes.
`:.vecF=0`