Question
An electron enters a region where magnetic field $$\left( B \right)$$ and electric field $$\left( E \right)$$ are mutually perpendicular, then
A.
it will always move in the direction of $$B$$
B.
it will always move in the direction of $$E$$
C.
it always possess circular motion
D.
it can go undeflected also
Answer :
it can go undeflected also
Solution :
The force experienced by a charged particle moving in space where both electric and magnetic fields exist is called Lorentz force.
Due to both electric and magnetic fields, the total force experienced by the charged particle will be given by,
$$\eqalign{
& F = {F_e} + {F_m} = qE + q\left( {v \times B} \right) \cr
& = q\left( {E + v \times B} \right) \cr} $$
When $$v,E$$ and $$B$$ are mutually perpendicular to each other. In this situation, if $$E$$ and $$B$$ are such that $$F = {F_e} + {F_m} = 0,$$ then acceleration in the particle, $$a = \frac{F}{m} = 0.$$
It means particle will go undeflected.