Question

what is the velocity of an electron that is in an electric field parallel to the trajectory of the electron?

Answer 1

`v= (qE)/(m)t+u`

Step-by-step explanation:

Given that, the electron is moving parallel to the electric field.

Then the electron experience a force which is given by,

`F=qE`

Therefore,

`ma=qE\\a=(qE)/(m)`

And q=e, and the acceleration is defines as,

`a=(d^(2)r )/(dt^(2) )`

Here, r is the the path traced by an electron.

Now equate the acceleration.

`(d^(2)r )/(dt^(2) )=(eE)/(m)`

Now integrate both side with respect to t.

`(dr)/(dt)= (eE)/(m)t+C`

Now, consider at t=0 the initial velocity of electron is u.

`u=(eE)/(m)(0)+C\\C=u`

Therefore the velocity of an electron is,

`v= (eE)/(m)t+u`