Question

What is velocity selector mentioned in the passage?

• A. Electric and magnetic field crossed to each other and electric field parallel to motion of the particles and $E=vB$
• B. Electric and magnetic field crossed to each other and magnetic field parallel to motion of the particle and $v=\frac{B}{E}$
• C. Magnetic field, electric field and velocity mutually perpendicular so that $v=\frac{E}{B}$
• D. Magnetic field, electric field and velocity mutually perpendicular so that $v=\frac{B}{E}$

Answer 1

The correct option is C Magnetic field, electric field and velocity mutually perpendicular so that $v=\frac{E}{B}$

The velocity selector allows the particles with a fixed speed $v=\frac{E}{B}$ only.
In velocity selector two kinds of forces exist. one is electric force $F_1=qE$ and another is magnetic force $F_2=qvB$. The idea is that, if the two forces are equal and opposite, the net force is zero, and the particle passes through the region without changing direction. Any particle having value of speed different than $\frac{E}{B}$ will deviate from its path and will not be able to pass through the slit as shown in the diagram in the question.
$F_1=F_2\Rightarrow qE=qvB$
$⟶v=\frac{E}{B}$