Question

In a certain region of space electric field $\overrightarrow{E}$and magnetic field $\overrightarrow{B}$ are perpendicular to each other. An electron enters in the region perpendicular to the direction of $\overrightarrow{B}$ and $\overrightarrow{E}$ both. If it moves un-deflected, then velocity of the electron is:

• A. $\frac{\left|\overrightarrow{E}\right|}{\left|\overrightarrow{B}\right|}$
• B. $\overrightarrow{E}\times \overrightarrow{B}$
• C. $\frac{\left|\overrightarrow{B}\right|}{\left|\overrightarrow{E}\right|}$
• D. $\overrightarrow{E}\overrightarrow{B}$

Answer 1

Answer: (A)

$\frac{\left|\overrightarrow{E}\right|}{\left|\overrightarrow{B}\right|}$

For the electron to pass undeflected, electric force on electron will equal and in opposite direction to that of the magnetic force.
$\left|\overrightarrow{F_e}\right|=\left|\overrightarrow{F_B}\right|$
$\therefore \left|q\overrightarrow{E}\right|=\left|q\right(\overrightarrow{v}\times \overrightarrow{B}|$
$\Rightarrow \left|\overrightarrow{v}\right|=\frac{\left|\overrightarrow{E}\right|}{\left|\overrightarrow{B}\right|}$