Question

The magnatic force acting on a charged particle of charge $-2\mu \text{C}$ in a magnatic field of $2\text{T}$ acting in $y$- direction, when the particle velocity is $(2\hat{i}+3\hat{j})\times {10}^6{\text{ms}}^{-1}$ is

• A. $8\text{N}$ in $z$- direction
• B. $8\text{N}$ in $-z$ direction
• C. $4\text{N}$ in $z$- direction
• D. $8\text{N}$ in $y$- direction

Answer 1

The correct option is B $8\text{N}$ in $-z$ direction

$\overrightarrow{F}=q(\overrightarrow{v}\times \overrightarrow{B})$

$q=2\mu \text{C}$

$\overrightarrow{v}=(2\hat{i}+3\hat{j})\times {10}^6{\text{ms}}^{-1}$

$\overrightarrow{B}=2\text{T}\hat{j}$

$\overrightarrow{F}=-2\times {10}^{-6}\left[\right(2\hat{i}+3\hat{j})\times 2\hat{j}]\times {10}^6$

$\overrightarrow{F}=-2\left(4\hat{k}\right)$

$\overrightarrow{F}=8(-\hat{k})$

Hence, option $\left(b\right)$ is the correct answer.