If the magnetic field is parallel to the positive Y-axis and the charged particle is moving along the positive X-axis as per figure, which way would the Lorentz force be for (a) an electron (negative charge), (b) a proton (positive charge).

Explanation

1. Lorentz force (here magnetic force) exerted on a charge q moving with velocity `vecv` in a uniform magnetic field `vecB` is given by,
`vecF_(m)=q(vecvxxvecB)" "...(1)`
2. For an electron, q = - e and so as per the diagram,
`vecF_(m)=-e(vecvxxvecB)`
= `e(vecBxxvecv)`
= `e[B(hatj)xxv(hati)]` (From the diagram)
`evB(hatjxxhati)`
`thereforevecF_(m)=evB(-hatk)`
`rArrvecF_(m)` on electron is along - Z-axis.
3. For a proton, q = +e and so from equation (1),
`vecF_(m)=e(vecvxxvecB)`
= `e[v(hati)xxB(hatj)]` (From the diagram)
= `evB(hatixxhatj)`
`thereforevecF_(m)=evB(hatk)`
`rArrvecF_(m)` on proton is along + Z-axis.