Question
In a certain region of space electric field $$E$$ and magnetic field $$B$$ are perpendicular to each other and an electron enters in region perpendicular to the direction of $$B$$ and $$E$$ both and moves undeflected, then velocity of electron is
A.
$$\frac{{\left| E \right|}}{{\left| B \right|}}$$
B.
$$E \times B$$
C.
$$\frac{{\left| B \right|}}{{\left| E \right|}}$$
D.
$$E \cdot B$$
Answer :
$$\frac{{\left| E \right|}}{{\left| B \right|}}$$
Solution :
For electron to pass undeflected, electric force on electron = magnetic force on electron
i.e. $$eB = evB$$
$$\eqalign{
& {\text{or}}\,\,v = \frac{E}{B}\,\, \cr
& {\text{or}}\,\,v = \frac{{\left| E \right|}}{{\left| B \right|}} \cr} $$