Question

A magnetic field of $(4\times10^{-3}\,\hat{k})\,T$ exerts a force of $(4\hat{i}+3\hat{j})\times10^{-10}N$ on a particle having charge of $1\times10^{-9}C$ and moving in x-y plane. Find the velocity of the particle.

• A. $(75\hat{i}+100\hat{j})\,ms^{-1}$
• B. $(75\hat{i}-100\hat{j})\,ms^{-1}$
• C. $(-75\hat{i}+100\hat{j})\,ms^{-1}$
• D. $(-75\hat{i}-100\hat{j})\,ms^{-1}$

Answer 1

Answer: (C)

As $\overrightarrow{F} = q(\overrightarrow{v} \times \overrightarrow{B})$
$\therefore $ $(4 \hat{i} + 3\hat{j}) \times 10^{-10} = 10^{-9}[(v_x \, \hat{i} + v_y \, \hat{j}) \times ( 4 \times 10^{-3} \hat{k})]$
Solving, $v_x$ = - 75 m/s and $v_y$ = 100 $ms^{-1}$
$\therefore $ Required velocity is $(- 75i + 100j)\, ms^{-1} $.