Question

A particle with ${10}^{-11}$ coulomb of charge and ${10}^{-7}$ kg mass is moving with a velocity of ${10}^8$ m/s along the y-axis. A uniform static magnetic field B = 0.5 T is acting along the x-direction. The force on the particle is

• A. $5\times {10}^{-11}Nalong\hat{i}$
• B. $5\times {10}^{3}Nalong\hat{k}$
• C. $5\times {10}^{-11}Nalong\hat{j}$
• D. $5\times {10}^{-4}Nalong-\hat{k}$

Answer 1

The correct option is D $5\times {10}^{-4}Nalong-\hat{k}$

By using $\overrightarrow{F}=q(\overrightarrow{v}\times \overrightarrow{B})$ ; where $\overrightarrow{v}={10}^8\hat{j}$ and $\overrightarrow{B}=0.5\hat{i}$
$\Rightarrow \overrightarrow{F}={10}^{-11}({10}^8\hat{j}\times 0.5\hat{i})=5\times {10}^{-4}(\hat{j}\times \hat{i})=5\times {10}^{-4}(-\hat{k})i.e.,5\times {10}^{-4}N$ along $-\hat{k}$