A particle of charge `qgt0` is moving at speed v in the +z direction through a region of uniform magnetic field. The magnetic force on the particle `vec F = F_0 (3 hat i + 4 hat j)`, where `F_0` is a positive constant.
(a) Determine the components `B_x, B_y` and `B_z` or at least as many of the three components as is possible from the information given.
(b) If it is given in addition that the magnetic field has magnitude `6F_0 / (qv)` , determine the magnitude of `B_z`.

Explanation

(a) `vecF=qvecvxxvecB=q |[hati ,hatj ,hatk],[v_x, v_y, v_z],[B_x ,B_y ,B_z]|=q |[hati ,hatj ,hatk],[0, 0, 0],[B_x ,B_y ,B_z]|`
`-qvB_xhati+qvB_xhati`
But `vecF=3F_0hati+4F_0hatj`,
So, `3F_0=-qvB_y` and `4F_0=qvB_x`
`B_y=-(3F_0)/(qv), B_x=(4F_0)/(qv), B_z` is arbitrary
(b) `B=(6F_0)/(qv)=sqrt(B_x^2+B_y^2+B_z^2) implies B_z=+-(11F_0)/(qv)`.