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
$\vec{v}\cdot \vec{a}=0$
$(2\hat{i}+c\hat{j})\cdot (3\hat{i}+4\hat{j})=0$
$\Rightarrow 6+4c=0$
$\Rightarrow c=-1.5$