Expert: Daniel Mazur - 11/24/2007

Question
QUESTION: if a point charge is released in a non uniform electric field with field lines in
the same direction then will it be in rectelinear motion?

ANSWER: Hello Aliya.
I will take this definition:
"rectilinear = Distance, paths, lines, etc. which are always parallel to axes at right angles. For example, a path along the streets of Salt Lake City or the moves of a rook in chess."
When one speaks of non-uniform electric field, one usually means that both (!) magnitude and direction of the maximum gradient are allowed to vary between points in space. This is the most general case of field. It naturally results in the most general motion of the test charge, which is certainly NOT rectilinear.
Cheers!
Daniel

---------- FOLLOW-UP ----------

QUESTION: thanks a lot sir for explaining in such a nice way but here one thing is making
me confuse that field lines are in the same direction.what does it mean?only
magnitude of electric field is changing?if this id the case then will charge
move in rectilinear ?

Answer
The problem is stated in a bit confusing way, but I think we can clear ti up. I think the problem is, how to interpret "with field lines in the same direction". The only consistent meaning of this is that the field lines at the point of the charge release (!) are pointing in the direction of the initial velocity. Of course, in a non-uniform field the filed lines are not straight lines (that pretty much follows from the definition) and so the motion away from the point of release will not go in the same direction as at the beginning.

The problem can be confusingly interpreted as concerning "non-uniform electric field with PARALLEL field lines", which is an obvious paradox. Like I said, only uniform field  has parallel field lines. Field lines are lines connecting points in space so that the vector of electric field E is always tangential to the field lines. Or, if you draw equipotential curves, the fields lines will be perpendicular to the equipotentials  in every point in space. A non-uniform field has curved equipotentials and thus curved field lines. The motion there cannot be rectilinear.

Take care.
Daniel