Question

Write the relation for the force `vecF` acting on a charge carrier q moving with a velocity `vec` through a magnetic field `vecB` in vector notation. Using the reltation, deduce the conditions under which this force will be (i) maximum (ii) minimum.

Answer 1

`vecF=q(vecvxxvecB)`
or `|vecF|=q|vecvxxvecB|=qvB sin theta`
(i) F will be maximum, when `sin theta=1` or `theta=90^@`, i.e., the charged particle is moving perpendicular to the direction of magnetic field.
(ii) F will be minimum, When `sin theta=0` or `theta=0^@` or `180^@` i.e., the charged particle is moving parallel to the direction of magnetic field.