Question

Velocity and acceleration vectors of charged particle moving perpendicular to the direction of a magnetic field at a given instant of time are $\vec{ v }=2 \hat{ i }+c \hat{ j }$ and $\vec{ a }=3 \hat{ i }+4 \hat{ j }$ respectively. Then the value of $c$ is

• A. 3
• B. 1.5
• C. -1.5
• D. -3

Answer 1

Answer: (C)

When a charged particle moves perpendicular to the magnetic field, it follows a circular path. On the circular path its velocity and acceleration will be at right angle to each other.
Given, $\vec{ v }=2 \hat{ i }+c \hat{ j }, \, \vec{ a }=3 \hat{ i }+4 \hat{ j }$
As $\vec{ v }$ and $\vec{ a }$ are perpendicular, hence
$\vec{ v } \cdot \vec{ a }=0$
$(2 \hat{ i }+c \hat{ j }) \cdot(3 \hat{ i }+4 \hat{ j })=0$
$\Rightarrow 6+4 c=0$
$\Rightarrow c=-1.5$