Do charges travel along field lines?

[Durin]

Hi. I'm a student in AP Physics this year and we started the E&M portion this week and we learned about electric fields.

I was watching MIT's OpenCourseWare in order to get more comfortable with the concepts. The lecturer said that charges do not follow electric field lines because of the forces on the charge could cause it to move onto a different field line, but I thought the forces are what caused the field lines to be shapped in the manner they are. So I'm curious if I was either misunderstanding the lecturer or my idea was wrong, and if so why are the field lines "curved" like a trajectory.

 

[diazona]

Long explanation coming up, just bear with me

Think about it like this: the electric field is a vector-valued function of position. That is, there is an imaginary vector at every point in space, and all these vectors constitute the electric field. At each point, the vector at that point represents the electric force per unit charge that would be acting on a charge at that point. So if you took a charged particle, put it at some point in space, and measure the force required to hold it there, that would tell you the magnitude and direction of the electric field at that point.

Now, one way to get the "big picture" of an electric field would be to do that measurement at a whole bunch of points, maybe every point on a 1000x1000x1000 grid in some region of space. That would give you a billion vectors that you could then draw out on a piece of paper (well, actually you'd probably get a computer to plot them) to get an image of this field. But with all those vectors, your drawing is going to get very crowded - you'll have a vector at one point running into the next point, and so on. So you might as well connect them. You can draw a curve that runs tangent to the electric field at all the points it passes through, and that is an electric field line. The direction of the field line at any point tells you the direction of the field at that point.

Remember that the electric field is related to force, and force in turn is related to acceleration. So when you know the direction of the electric field at a point, you know the direction that a charged particle would accelerate if it were at that point. But the particle doesn't automatically move in the same direction it's accelerating in. If the field points up, and the particle starts out moving sideways, sure its trajectory is going to be bent upwards a little bit (if it's a positively charged particle), but that doesn't mean it stops moving sideways. In general, the trajectory a particle moves on is determined by its initial velocity as well as any forces (like the electric force) that act on it.

 

[mensa]

I've been thinking since u gave this out. I totally agree with the words in #2. But I suggest that this may because the charge can change the field.
I've downloaded all the physics courses in OCW but haven't finished then yet. It may help if you tell in which course and at what time.

 

[Durin]

Long explanation.

Thanks that really helped the picture in my head. So my question. I suppose I should ask now is what if it's placed along these lines with an intial velocity of zero would it still not follow the lines like a trajectory?

And, mensa, it's in the second lecture at which point I'm not sure. I think it's toward the middle.

 

[Bob S]

Thanks that really helped the picture in my head. So my question. I suppose I should ask now is what if it's placed along these lines with an intial velocity of zero would it still not follow the lines like a trajectory?

Yes, if the field lines are straight. If they are curved, then a particle with charge and mass will have a momentum (velocity) that is not aligned with the acceleration (force).
Bob S

 

[diazona]

Yep, exactly what Bob S said.

To clarify, if you put a particle in an electric field with initial velocity 0, at the very first moment when it started to move, its motion would be aligned with the field line. But once it starts moving in that direction, if the field line curves away, the particle will not follow it.

 

[Durin]

Okay thank you for the help. It all makes sense now.