Question

An electron moves with speed $2\times {10}^{5}m/s$ along the positive x-direction in the presence of a magnetic induction $B=\hat{i}+4\hat{j}-3\hat{k}$ (in Tesla.) The magnitude of the force experienced by the electron in Newton's is (charge on the electron = $1.6\times {10}^{-19}$ C)

• A. $1.18\times {10}^{-13}$ N
  
• B. $1.28\times {10}^{-13}$ N
  
• C. $1.6\times {10}^{-13}$ N
  
• D. $1.72\times {10}^{-13}$ N

Answer 1

The correct option is C $1.6\times {10}^{-13}$ N


$\overrightarrow{v}=2\times {10}^5\hat{i}$ and $\overrightarrow{B}=(\hat{i}+4\hat{j}-3\hat{k})$
$\overrightarrow{F}=q(\overrightarrow{v}\times \overrightarrow{B})=-1.6\times {10}^{-19}[2\times {10}^5\hat{i}\times (\hat{i}+4\hat{j}-3\hat{k}\left)\right]$
$=-1.6\times {10}^{-19}\times 2\times {10}^5[\hat{i}\times \hat{i}+4(\hat{i}\times \hat{j})-3(\hat{i}\times \hat{k}\left)\right]$
$=-3.2\times {10}^{-14}[0+4\hat{k}+3\hat{j}]=3.2\times {10}^{-14}(-4\hat{k}-3\hat{j})$
$\Rightarrow \left|\overrightarrow{F}\right|=3.2\times {10}^{-14}\times 5=1.6\times {10}^{-13}N$.