Question

A charged particle carrying charge $1\mu C$ is moving with velocity $(2\hat{i}+3\hat{j}+4\hat{k})m{s}^{-1}$. If $an$ external magnetic field of $(5\hat{i}+3\hat{j}-6\hat{k})\times 10^{-3}T$ exists in the region where the particle is moving then the force on the particle is $\overrightarrow{F}\times 10^{-9}N$. The vector $\overrightarrow{F}$ is :

• A. $-0.30\hat{i}+0.32\hat{j}-0.09\hat{k}$
• B. $-300\hat{i}+320\hat{j}-90\hat{k}$
• C. $-30\hat{i}+32\hat{j}-9\hat{k}$
• D. $-3.0\hat{i}+3.2\hat{j}-0.9\hat{k}$

Answer 1

Answer: (C)

$\overrightarrow{F}=9(\overrightarrow{V}\times \overrightarrow{B})$ (Force on charge particle moving in magnetic field)
$\overrightarrow{V}\times \overrightarrow{B}=(2\hat{i}+3\hat{j}+4\hat{k})\times (5\hat{i}+3\hat{j}-6\hat{k})\times 10^{-3}$
$=\left(\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 3& 4\\ 5& 3& -6\end{array}\right)\times 10^{-3}$
$=[\hat{i}[-18-12]-\hat{j}[-12-20]+\hat{k}[6-15]]\times 10^{-3}$
$=[\hat{i}[-30]+\hat{j}[32]+\hat{k}[-9]]\times 10^{-3}$
Force $=10^{-6}[-30\hat{i}+32\hat{j}-9\hat{k}]\times 10^{-3}$
$=10^{-9}[-30\hat{i}+32\hat{j}-9\hat{k}]$