Attaining speed of light with electric field

[zorro]

I got this doubt while solving a problem.
Suppose an electron starts moving from rest in a region of very high electric field of the order or 10⁶V/m along its direction.

Its acceleration is given by a=Eq/m, which is 1.758 x 10¹⁷m/s² on substitution. We can ignore 'g' here.

The time taken to attain the speed of light is t = v-u/a = v/a = 1.71 x 10^-9 s

How is it possible?

 

[cepheid]

Are you wondering why the time required is so short, or are you wondering why the electron achieves the speed of light at all when that is supposed to be impossible? The answer to the first question is that that is a tremendously large electric field and hence is produces a tremendously large acceleration that, in *classical* physics, would cause the electron to reach c very quickly. The answer to the second question is that in special relativity, a = F/m is not quite true, and is modified in such a way that no massive object can reach c.

 

[tiny-tim]

Hi Abdul!

(try using the X² icon just above the Reply box )

Its acceleration is given by a=Eq/m …

No, the correct formula is d/dt (momentum) = Eq …

so the https://www.physicsforums.com/library.php?do=view_item&itemid=53" can get infinitely large, but the speed stays less than c.

(for small speeds, of course, d/dt (momentum) is approximately ma)

 

[zorro]

Ah, I still did not study special relativity. Thank you cepheid and tiny-tim.