# Question about the motion charges moving within an electric field

1. Jan 18, 2012

### Excalibur1152

I've almost certain that I have read/ seen from MIT's OCW that the motion of a charge within an electric field does not follow the field lines.

Today my physics teacher said the opposite, that the path of motion of a charge within a field will follow a field line.

Who is right? And why?

EDIT: I meant to put an 'of' in between the 'motion' and 'charges' in the title.

2. Jan 18, 2012

### sophiecentaur

If the charge started off with no velocity then it will 'fall' along field lines just the same as a dropped object falls vertically on Earth. If the object was originally moving then it will follow a trajectory, accelerating in the direction of the field lines, and its velocity will always be the (vector) sum of its original velocity and the velocity in the direction of the force due to the field. For a uniform field, the shape of path will be part of a parabola.

3. Jan 18, 2012

### Excalibur1152

So if I were to place a (positive) charge on top of one of the field lines ^^^ without giving it an initial velocity, it would never leave the line? It's path would only exist upon the same field line?

(I know that there are an infinite # of lines, but as far as the picture is concerned)

4. Jan 18, 2012

### sophiecentaur

Right - that diagram has made me think again! I was considering, initially, straight field lines (point source or between plates).

If the lines are curved then you would expect the velocity of the charged object, once it had been accelerated at all, would not be parallel to the lines of force so it would move through them and not follow just one line. The degree that it would depart from the line it 'started on' would presumably depend upon the ratio of the charge of the object to its mass. If it had no mass then it would follow the line.

5. Jan 18, 2012

### Excalibur1152

Indeed, if the field lines are straight, then the charge should only move along the field lines.

If the charge does have mass, it gains kinetic energy, and so when the field line curves, then work has to be done over a distance to "change" the path of motion? Wouldn't this distance be the distance that the charge moves out of the field line? (maybe not that simple, but hopefully you can still follow my logic).

As an example, if you put a positive charge with mass right between the two charges on the dipole I posted earlier (but imagine that both are positive charges, so three positive charges total), but moved it closer to one of the charges, wouldn't it oscillate between them? If it did that, then wouldn't it be moving against a field line?

Much thanks for responding to my posts.

6. Jan 18, 2012

### sophiecentaur

It's a conservative field so kinetic plus potential energy will be constant, so yes it could go 'uphill' at times.