Question

An electron is moving along $+x$ direction with a velocity of $6\times {10}^6{\text{ms}}^{-1}$. It enters a region of uniform electric feild of $300\text{V/cm}$ pointing along $+y$ direction of the magnetic feild set up in this region such that electron keeps moving along the $+x$ direction will be:

• A. $3\times {10}^{-4}\text{T},$ along $+z$ direction
• B. $5\times {10}^{-3}\text{T},$ along $-z$ direction
• C. $5\times {10}^{-3}\text{T},$ along $+z$ direction
• D. $3\times {10}^{-4}\text{T},$, along $-z$ direction

Answer 1

The correct option is C $5\times {10}^{-3}\text{T},$ along $+z$ direction

Given:
$\overrightarrow{E}=300\hat{j}\text{V/cm}=3\times {10}^4\text{V/m}$
$\overrightarrow{v}=6\times {10}^6\hat{i}\text{m/s}$


$\overrightarrow{B}\text{must be in +z axis.}$
So, $q\overrightarrow{E}+q\overrightarrow{v}\times \overrightarrow{B}=0$
$\Rightarrow E=vB$
$\therefore B=\frac{E}{v}=\frac{3\times {10}^4}{6\times {10}^6}=5\times {10}^{-3}\text{T}$
Hence, magnetic field $B=5\times {10}^{-3}\text{T}$ along $+z$ direction.