Question

A magnetic field $4\times {10}^{-3}\hat{k}T$ exerts a force $(4\hat{i}+3\hat{j})\times {10}^{-10}N$ on a particle having a charge ${10}^{-9}$C and going in the X-Y plane. The velocity of the particle is

• A. $-75\hat{i}+100\hat{j}$
• B. $100\hat{i}+75\hat{j}$
• C. $75\hat{i}+100\hat{j}$
• D. $100\hat{i}-75\hat{j}$

Answer 1

The correct option is A $-75\hat{i}+100\hat{j}$

$\overline{F}=q(\underset{V}{\to }\times \underset{B}{\to })$
$(4\hat{i}+3\hat{j})\times {10}^{-10}={10}^{-19}\left(\right(u\hat{i}+v\hat{j}+w\hat{k})\times (4\times {10}^{-3}\hat{k}\left)\right)$
$(4\hat{i}+3\hat{j})\times 25=-u\hat{j}+v\hat{i}$
comparing the cofficient
$u=-75;v=100$