Revered Members,
In the problem of motion of an electron in an electric field , we take the initial velocity of electron in the vertically upward direction is zero. Can i know why?

 

Can i know why?

No! It's a secret.

 

Which we know and you don't.

Hint, Electrons drift in their flow.

 

My textbook says motion of electron in an electric field is similar to projectile motion. In projectile motion, we assume the initial velocity to be zero for the following cases
1) When the body starts from rest
2) If a body is dropped from a height.
But i can't correlate why the initial velocity is zero for an electron in its upward direction.

 

My textbook says motion of electron in an electric field is similar to projectile motion. In projectile motion, we assume the initial velocity to be zero for the following cases
1) When the body starts from rest
2) If a body is dropped from a height.
But i can't correlate why the initial velocity is zero for an electron in its upward direction.

It seems to me that you need to be given a description, from which you can deduce this assumption. In the absence of such information, I would take the statement as a given assumption.

Be aware, you are not giving us much information to go on. Also, the dynamics of an electron are governed by quantum mechanics and not classical mechanics. Hence, your limited information leads me to believe you are interested in assuming that classical mechanics can be applied to whatever problem you are dealing with.

In quantum mechanics, the statement that one velocity component is exactly zero would imply that you have no idea where the electron is, in position, via the uncertainty principle.

Personally, I can't help you much more than that without more information to go on.

 

Physics analysis often starts by looking at the simplest cases - one force, one mass, zero initial velocity.

Once that case has been described, then it can move to more complicated cases - multiple forces, non-zero initial velocities, etc.

Your textbook may just be assuming zero velocity to work out the simplest dynamics, leaving real-world cases for later analysis.

 

Thanks steveb and davebee.
@steveb: Can i presume since the initial velocity is zero in vertical upward direction, the position or momentum can't be determined accurately in that direction?

 

Thanks steveb and davebee.
@steveb: Can i presume since the initial velocity is zero in vertical upward direction, the position or momentum can't be determined accurately in that direction?

The knowledge that initial velocity is zero tells you that the momentum is zero in that direction and tells you nothing about the position in that direction.

As to whether or not you can determine the position by other means, the answer is no if you use quantum mechanics. The uncertainty principle tells you that if you know velocity (or momentum) exactly, then all positions are equally likely and you can say nothing about where the electron is in that direction.

If you allow yourself to use classical mechanics (which is dubious for an electron), then the position can be known exactly, but the knowledge of velocity being zero does not help you determine anything about position.

 

But classical mechanics are used for all kinds of practical problems involving electrons and electric fields.

If you are willing to say that the velocity is zero with a standard deviation of 0.05m/s, then you can claim knowledge of the position to about 1mm -- assuming I did the math right. I was actually surprised it was even up on this scale.