A charge q enters a region having electric field
E and magnetic field B with velocity v. If it continues to move with the same velocity, then which of the following statement is not true

Options

A. E.B=0
B. E.v=0
C. If v.B = 0.then v `=(ExxB)/(BxxB)`
D. v xx E = B

Answer

D

Explanation

Lorentz force on electron,
`F=q(E+v+B)`
For regular motion, F = 0
`rArr E+(vxxB)=0`
`rArr E||(vxxB), " also "[vxxB " is perpendicular to both v and B"]`
Now, E `_|_` v and E `_|_` B [(i) and (ii) are right ]
`rArr` E.v = 0 and E.B = 0
Now, if v.B = 0 `rArr v_|_ B`
So, E `_|_ v _|_ B`
E= v xx B
E xx B = (v xx B) xx B
`v xx B = vB hat(n)`
`rArr (vB)xxB=v(B.B)`
`rArr v=(ExxB)/(B.B)` [is right]
Now, E = v xx B
`v xx E = v xx vxxB= 0 hneB`
So, option (d) is wrong.