Question

A charged particle carrying charge $1 \mu C$ is moving with velocity $(2 \hat{ i }+3 \hat{ j }+4 \hat{ k }) ms ^{-1}$. 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)
$\overrightarrow{ V } \times \overrightarrow{ B }=(2 \hat{ i }+3 \hat{ j }+4 \hat{ k }) \times(5 \hat{ i }+3 \hat{ j }-6 \hat{ k }) \times 10^{-3}$
$=\begin{pmatrix}\hat{i}&\hat{j}&\hat{k}\\ 2 &3&4\\ 5&3&-6\end{pmatrix}\times10^{-3}$
$=[\hat{ i }[-18-12]-\hat{ j }[-12-20]+\hat{ k }[6-15]] \times 10^{-3}$
$=[\hat{ i }[-30]+\hat{ j }[32]+\hat{ k }[-9]] \times 10^{-3}$
Force $=10^{-6}[-30 \hat{ i }+32 \hat{ j }-9 \hat{ k }] \times 10^{-3}$
$=10^{-9}[-30 \hat{ i }+32 \hat{ j }-9 \hat{ k }]$