# Lines of force?

1. Jun 21, 2009

### siddharth5129

Do the electric lines of force necessarily depict the trajectory of a charged particle? Or do they depict the trajectory at all.

2. Jun 21, 2009

### dx

The electric lines of force are representations of the electric field. They are not the trajectories that charged particles take.

3. Jun 21, 2009

### gnurf

From the definition of the electric field intensity

$$\vec{E}=\frac{\vec{F}}{q}$$

you'll see that the force experienced by a charged particle placed in an electric field is in the same direction (if the charge is positive) as that of the electric field everywhere where the field is present.

This means that the electric field lines do in fact depict the trajectory of a charged particle, but only as long as there are no other forces also acting on the particle.

4. Jun 21, 2009

### Staff: Mentor

No. As dx said, the lines represent the direction of the electric force (on a positive charge), not the direction of the particle's velocity.

5. Jun 21, 2009

### gnurf

What I was trying to say was that a charged particle (initially at rest) will move along the electric field lines if no other forces are acting on the particle. Is this wrong?

6. Jun 21, 2009

### dx

Yes, that's wrong. Just think about this: what if you initially throw a particle perpendicular to a field line?

An even more familiar example: The gravitational field lines near the Earth's surface are vertical lines pointing downwards. Does that mean that particles near the earth always move vertically downwards?

7. Jun 21, 2009

### Staff: Mentor

OK, being at rest is a special case. If it starts from rest it will initially move in the direction of the field lines.

8. Jun 21, 2009

### gnurf

I stand corrected:

It's the charged particle's acceleration $$\vec{a}$$ that points in the direction of the force $$\vec{F}$$ , and hence the electric field $$\vec{E}$$ at a point. The velocity $$\vec{v}$$ is then in the direction of the tangential of the trajectory. This is why, as Doc Al pointed out, that $$\vec{v}$$ and $$\vec{E}$$ only point in the same direction when $$\vec{v} = 0$$ (e.g., initially at rest).

In the general case the trajectory of a charged particle will not follow the electrical field lines.

Sorry for messing that up.

Last edited: Jun 21, 2009
9. Jun 24, 2009

### siddharth5129

So , say the electric lines of force are curved , as in an electric dipole , then the direction of force on the charged particle varies continuously. Then , if I'm not wrong , this will not necessarily change the direction of velocity on the said particle to cause it to follow the electric field line? ............. Why exactly ?