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A charged particle with charge q enters ...

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

A

`vecv=vecE xx vecB //B^(2)`

B

`vecv=vecB xx vecE//B^(2)`

C

`vecv=vecE xx vecB//E^(2)`

D

`vecv=vecB xx vecE//E^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`vecF_("net")=vecF_(e )+vecF_(m)`
`0=q vecE+q(vecv xx vecB)`
`rArr vecE=vecB xx vecv rArr vecE xx vecB= (vecB xx vecv) xx vecB`
`=(vecB.vecB)vecv-(vecB.vecv)vecB`
`:. ` B, E & v are mutually `bot` as given
`rArr vecv =(vecE xx vecB)/(B^(2))`
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