Question

An electric charge `+q` moves with velocity `vecv=3hati+4hatj+hatk`, in an electromagnetic field given by `vecE=3hati+hatj+2hatk`, `vecB=hati+hatj-3hatk`.
The y-component of the force experienced by +q is
A. `2q`
B. `11q`
C. `5q`
D. `3q`

Answer 1

Correct Answer - B
`vecF=qvecE+q[vecvxxvecB]`
`=qvecE+q[(3hati+4hatj+hatk)xx(hati+hatj-3hatk)]`
`=qvecE+q|hati hatj hatq|hati hatj hatk`
3 4 1
1 1 -3
`=q(3hati+hatj+2hatk)+q[hati(-12-1)+hatj(1+9)+hatk(3-4)]`
`=q[-10hati+11hatj+hatk] :. F_y=11q`