A charged particle with charge `q` enters a region of constant, uniform and mututally orthogonal fields `vec(E) and vec(B)` with a velocity `vec(v)` perpendicular to both `vec(E) and vec(B)`, and comes out without any change in magnitude or direction of `vec(v)`. Then

Options

A. `vecv=vecExxvecB//B^(2)`
B. `vecv=vecExxvecE//B^(2)`
C. `vecv=vecExxvecE//E^(2)`
D. `vecv=vecBxxvecE//E^(2)`

Answer

1

Explanation

`qvecvxxvecB=qvecE`...(1)
Taking cross product of equation `(1)` with `vecB`
`q(vecvxxvecB)xxvecB=q(vecExxvecB)`
`vecv=vecExxvecB//B^(2)`