Question

A proton is moving in a gravity free space having a uniform electric field $E$ of unknown magnitude and direction. There is a uniform magnetic field of $0.01\text{T}$ pointing in the $y$ - direction. The proton moves in the $x$ - direction at a constant velocity of $10\text{km/s}$ . All directions are with respect to the usual right handed $x-y-z$ coordinate system. Which of the following is /are correct ?

• A. $E_z=100\text{V/m}$
• B. $E_z=-100\text{V/m}$
• C. $E_y=100\text{V/m}$
• D. $E_x=0\text{V/m}$

Answer 1

Answer: (B), (D)

$E_x=0\text{V/m}$


Using Lorentz equation, ${\overrightarrow{F}}_{net}=-e\overrightarrow{E}+-e[\overrightarrow{V}\times \overrightarrow{B}]$

In this case , ${\overrightarrow{F}}_{net}=0$

$\Rightarrow \overrightarrow{E}=-\overrightarrow{v}\times \overrightarrow{B}=-(10,000\hat{i}\times 0.01\hat{j})$

$\Rightarrow \overrightarrow{E}=-100\hat{k}$

$\Rightarrow {\overline{E}}_x=0;E_y=0;E_z=-100$

Hence, options (b) and (d) are the correct answers.