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# Engineering

A charged particle carrying charge 1\mu C is moving with velocity \left ( 2\hat{i}+ 3\hat{j}+4\hat{k} \right )ms^{-1}. If an external MF of \left ( 5\hat{i}+3\hat{j}-6\hat{k} \right )\times 10^{-3}T  exists in the region where the particle is moving then the force on the particle is \underset{F}{\rightarrow}\times 10^{-9}N The vector \underset{F}{\rightarrow} is    
Option: 1 0.3\hat{i}+0.32\hat{j}-0.09\hat{k}
 
Option: 2 -30,32,-9
Option: 3 -300,+320,-90  
Option: 4 -3,+3.2,-0.9

Answers (1)
A avinash.dongre

\\ given, \ q=1 \mu C=1 \times 10^{-6}C\\ \vec{v}=2\hat{i}+3\hat{j}+4\hat{k}\\ \vec{B}=(5\hat{i}+3\hat{j}-6\hat{k})\times 10^{-3}T\\ \text{We know that, }\\ \vec{F}=q(\vec{v} \times \vec{B})\\ \Rightarrow \vec{F} \times 10^{-9}=10^{-6} [(-18-12)\hat{i}-(-12-20)\hat{j}+(6-15)\hat{k}] \times 10^{-3}\\ \Rightarrow \vec{F}=-30\hat{i}+32\hat{j}-9\hat{k}

So, option 2 is correct.

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