KVPY Sample Paper KVPY Stream-SX Model Paper-18

A charged particle projected perpendicularly into a magnetic field of \[(7\hat{i}-3\hat{j})\times {{10}^{-\,3}}\] tesla acquires an acceleration of \[(x\hat{i}+7\hat{j})m{{s}^{-\,2}}.\] The value of x is-

A) 2 m

B) 3 m

C) 4 m

D) 7 m

Correct Answer: B

Solution :

\[{{\vec{F}}_{m}}=q\vec{v}\times \vec{B}\]

\[m\vec{a}=q\vec{v}+\vec{B}\]

\[\Rightarrow \vec{a}\bot \vec{v}\] so \[\vec{a}.\vec{v}=0\]

\[\Rightarrow (x\hat{i}+7\hat{j}).(7\hat{i}-3\hat{j})\times {{10}^{-3}}=0\]

\[7x-21=0\]

\[x=3\]