Question

In the given figure, $E$ and $B$ are magnitudes of electric and magnetic fields which are acting on a moving electron as shown. The direction of velocity of electron is along $X$-axis. Then, force on electron is given by

• A. $F =q(E+v B) \hat{ j }$
• B. $F =q(E-v B) \hat{ j }$
• C. $F =q(E+v B) \hat{ k }$
• D. $F =q(E-v B) \hat{ k }$

Answer 1

Answer: (B)

When electric and magnetic fields are perpendicular to each other.
So,$F _{E} =q E =q E \hat{ j }, F _{B}=q v \times B $
$=q(\hat{ i } \times B \hat{ k })=-q v \hat{ j }$
$(\because \hat{ i } \times \hat{ k }=-\hat{ j })$
Therefore, force on electron is given by
$F =q(E-v B) \hat{ j }$