What is constant velocity? This is in a question of moving charge.

[yungman]

This is in a question of finding retarded potential where the point charge is moving at constant velocity.

The book let the charge pass through the origin at t=0 so $$\vec w(t) = \vec v(t)$$ which I don't understand.

This might be a stupid question. velocity is a vector with amplitude and direction. So what is the meaning of constant velocity?

Of cause I know |v|= constant, but does constant velocity implies it travel in a straight line because traveling in a curve is not consider constant velocity?

 

[khemist]

A constant velocity is one where the derivative of that motion is zero. Traveling in a curve would require an acceleration (if moving in a circle, that acceleration is v^2/r), in which case the derivative of that velocity would not be zero.

Regarding the w(t) = v(t), I assuming they just want to set up a situation where there was no acceleration to get to the velocity v.

And I think it would be more correct to say the velocity vector has a magnitude, rather than an amplitude. Amplitudes are found in wave functions. However, to determine if something has a constant velocity, one would either need the velocity function, or would have to take measurements of the velocity at different times. If one took the tangential velocity of a particle moving about a circle, each vector measured would be "straight," in the sense it only has a direction and magnitude, but if I measured the velocity again at another point, it would not be pointing in the same direction.

One cannot find the derivative of a vector through normal differentiation, I believe you need the covariant derivative for that (dont quote me here ;)).

 

[tiny-tim]

Of cause I know |v|= constant, but does constant velocity implies it travel in a straight line because traveling in a curve is not consider constant velocity?

simple answer …

yes ​

 

[yungman]

Thanks all.

 

[sardar]

Constant velocity refers to the motion of an object at a steady speed in a straight line. In the context of a moving charge, it means that the charge is moving at a consistent speed and in a consistent direction. This is important to consider when calculating the retarded potential, as the charge's velocity affects the strength and direction of the potential at different points in space.

In the context of the given scenario, the charge is passing through the origin at t=0, meaning it has a velocity vector \vec w(t) that is equal to its velocity vector \vec v(t). This simply means that the charge is moving at a constant velocity, and the direction of its velocity does not change over time.

It is important to note that constant velocity does not necessarily mean the object is moving in a straight line. It is possible for an object to have a constant velocity while moving in a curve, as long as the magnitude and direction of its velocity remains constant.

In summary, constant velocity refers to the steady motion of an object at a consistent speed and direction. In the context of a moving charge, it is important to consider when calculating the potential at different points in space.