An electron of mass $9.1 * 10^{-31}kg$ and charge $1.6 * 10^{-19}C$ is situated in a uniform electric field of intensity $1.2 * 10^{4}Vm^{-1}$. Find the time it takes to travel $1\; cm$ from rest.

Given,

Mass of electron  $(m_e) = 9.1 * 10^{-31}\;kg$

Charge of Electron $(q) = 1.6 * 10^{-19}\; C$

Electric Field Intensity $(E) = 1.2 * 10^{4}\; V/m$

Distance $(d) = 1 \; cm = 1 * 10^{-2} \; m $

Time $(t) = \;?$

We know that,

 

$F$   =    $q.E$   ⇒   $m.a$    =   $q.E$   ⇒   $a$    =   $\frac{q.E}{m}$   =    $\frac{(1.6 \; * \; 10^{-19})\;*\; (1.2\;*\;10^{4})}{9.1 \; * \;10^{-31}}$

∴ $a = 2.1 \; *\; 10^{15}\; m/s^2$

Now,

To calculate the time, we have

$S = ut + \frac{1}{2}at^2$     ⇒    $S = \frac{1}{2}at^2$    [∵ u = 0]

⇒ $t^2$   =   $\frac{2.S}{a}$     =    $\frac{2 \;*\; 1 \;* \; 10^{-2}}{2.1 * 10^{15}}$

∴ $t = 3.08 * 10^{-9} Sec $

Hence, it takes $3.08*10^{-9}\;$sec to travel 1 cm from rest.

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