# A charged particle carrying charge

Question:

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

N. The vector $\vec{F}$ is :

1. (1) $-0.30 \hat{i}+0.32 \hat{j}-0.09 \hat{k}$

2. (2) $-30 \hat{i}+32 \hat{j}-9 \hat{k}$

3. (3) $-300 \hat{i}+320 \hat{j}-90 \hat{k}$

4. (4) $-3.0 \hat{i}+3.2 \hat{j}-0.9 \hat{k}$

Correct Option: 1

Solution:

(1) [Given: $q=1 \mu C=1 \times 10^{-6} C$;

$\vec{V}=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \mathrm{m} / \mathrm{s}$ and

$\left.\vec{B}=(5 \hat{i}+3 \hat{j}-6 \hat{k}) \times 10^{-3} \mathrm{~T}\right]$

$\vec{F}=q(\vec{V} \times \vec{B})=10^{-6} \times 10^{-3}\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 2 & 3 & 4 \\ 5 & 3 & -6\end{array}\right|$

$=(-30 \hat{i}+32 \hat{j}-9 \hat{k}) \times 10^{-9} \mathrm{~N}$

$\therefore \vec{F}=(-30 \hat{i}+32 \hat{j}-9 \hat{k})$