Question

Velocity and acceleration vectors of a charged particle moving in a magnetic field at some instant are $\overrightarrow{v}=3\hat{i}+4\hat{j}$ and $\overrightarrow{a}=2\hat{i}+x\hat{j}$. Select the correct alternative(s) :

• A. $x=1.5$
• B. $x=3$
• C. magnetic field is along z-direction
• D. kinetic energy of the particle is constant

Answer 1

Answer: (A), (C), (D)

The correct options are
A $x=1.5$
C kinetic energy of the particle is constant
D magnetic field is along z-direction

Force & velocity are perpendicular to each other in magnetic field
So
$\overrightarrow{V}\cdot \overrightarrow{a}=0$
$(3\hat{i}+4\hat{j})\cdot (2\hat{i}+x\hat{j})=0$
$6+4x=0$
$x=-1.5$
No work is done by magnetic field. So, KE of particle is constant