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.

Mar 8, 2016

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 $\vec{v}$ in an external electric field $\vec{E}$ and magnetic field $\vec{B}$ is described by the Lorentz Force equation:

$\vec{F} = q \left(\vec{E} + \vec{v} \times \vec{B}\right)$

Given a proton moving West encounters a magnetic field going to East. As there is no external electric field, above equation reduces to
$\vec{F} = q \cdot \vec{v} \times \vec{B}$

As the velocity vector of proton and magnetic field vector are opposite to each other, angle $\theta$ between the two$= {180}^{\circ}$.
We know that $\sin {180}^{\circ} = 0$.
Consequently the cross product vanishes.
$\therefore \vec{F} = 0$