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What distance must an electron move in a uniform potential gradient 200V/cm in order to gain kinetic energy 3.21018J?


Given,
Potential Gradient (E) = 200V/cm = 200103V/m
Kinetic Energy (Ek)
Charge of Electron (q) = 1.61019C
Mass of Electron (m) = 9.11031kg
Distance (S) = ?

We know that,
F=m.a
 ⇒ a   =  Fm  =  q.Em   =   1.610192001039.11031   =   3.51015m/s2 
Now,
 EK=12m.v2
v2=2.Ekm   =   2(3.21018)(9.11031)    =   71012m/s

Again, to Calculate the distance,
v2=u2+2as                        [∵ u=0]
S=v22a   =   710122(3.51015)   =   0.001m
Hence,
The required distance is 0.001m.


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