# Magnetic field lines vs. Electric field lines

What's the difference between magnetic field and electric field lines?

Does $d\vec B$ point in the direction you would experience a force if you were a moving charged particle at that point? I know for a fact the electric field and electrostatic force are parallel, but since $F = q\ \vec v \times \vec B$ for magnetic forces. Does that actually mean though that if, say, in the following graphic:

Where the dot is a wire going in and out of the page, that the $d\vec B$ vectors are not showing how a moving charged particle will move in the field?

Basically, I feel justified in thinking electric field lines communicate how a test charge will move at any given point in space.

How can I juxtapose this with magnetic field lines>

• "electric field lines communicate how a test charge will move at any given point in space" - This is incorrect. Once the charge starts moving, the magnetic field lines also influence its motion, so the electric field lines alone do not tell you how the test charge will move. Apr 18 '18 at 16:35
• @probably_someone So, is an electron's trajectory truly extremely difficult to predict? Once it starts moving, can its movement then be influenced by its own magnetic field? Apr 18 '18 at 21:45
• No. It's also not all that difficult to predict, either; the force on an electron in an electromagnetic field is given by the Lorentz force: en.wikipedia.org/wiki/Lorentz_force. Taking $F=ma$ gives you a differential equation that you can solve to get the electron's trajectory. Apr 18 '18 at 21:49
• I was not aware of this, which I'm surprised by. Cheers! Apr 18 '18 at 21:52

If they existed, magnetic field lines point in the direction of the force experienced by a magnetic monopole (assuming only a B-field is present).

For electric monopoles (charges), if they are moving then the force they experience due to the magnetic field is always at right angles to the field lines. That is of course not a uniquely determined direction. The exact direction is determined by the particle charge and velocity, since the force must also be at right angles to the velocity.

Not exactly. Electric field lines represent forces that directly influence and are generated by electrically charged particles. Thus E-field lines describe the forces a charged particle would experience when exposed to them, but this is only true for electrostatics. Once the charged particles start to move, they generate magnetic fields, which influence moving electrically charged particles. Here the B-field lines do not directly represent the force experienced by the particles. However, the force experienced by an external moving charged particle does not necessarily follow the direction of the E-field that's generating the magnetic field.

For example, in your drawing the current flowing through the wire is coming out of the page towards you. That means the E-field is in the same direction. Normally the E-field would influence the particle on its own, but lets ignore that to see the influence by the B-field. If a negatively charged particle were to fly by the wire in the opposite direction to the current, it would be influenced by the B-field to move in a direction away from the wire. Which is not in the direction of the E-field.

So no, magnetic field lines do not directly indicate the direction of a force as far as moving charged particles are concerned, but magnetic fields do exert a force on them separately from the force the electric field would exert.

• "For example, in your drawing the current flowing through the wire is coming out of the page towards you. That means the E-field is in the same direction" This is not true. First, it all depends on the net charge in the wire (not net charge means $E=0$). Second, if we had a net charge in the wire, the electric field would point radially outward from the wire. It would not point in the direction of the wire. Aug 2 '18 at 16:06

What's the difference between magnetic field and electric field lines?

Electric field lines point in the direction a hypothetical test charge would move. By convention, it's a positive charge. In the presence of static electric fields only, $${\mathbf F} = q {\mathbf E}$$, so the arrows of the electric field lines are parallel to the electric force, so it's OK to call the former as lines of force (because they point in the direction of the force.

Magnetic field lines point in the direction the north pole of a hypothetical compass would point. In the presence of static magnetic fields only, $${\mathbf F} = q ({\mathbf v} \times {\mathbf B})$$, and since $$({\mathbf v} \times {\mathbf B})$$ is perpendicular to $${\mathbf B}$$, then the arrows of the magnetic field lines are perpendicular to the magnetic force, so it's a bad idea to call the former as lines of force (because they don't point in the direction of the force).

Does $$d\vec B$$ point in the direction you would experience a force if you were a moving charged particle at that point?

No. $$\mathbf B$$ is perpendicular to $${\mathbf F}_\text{m}$$, not parallel to it.

I know for a fact the electric field and electrostatic force are parallel

True.

but since $$F = q\ \vec v \times \vec B$$ for magnetic forces, does that actually mean though that if, say, in the following graphic, where the dot is a wire going in and out of the page, that the $$d\vec B$$ vectors are not showing how a moving charged particle will move in the field?

Exactly. $$\mathbf B$$ doesn't show the direction of the magnetic force nor the direction of the path taken by the charged particle. It shows the direction the north pole of a compass would point to.

The electric and magnetic fields are real things: they can store energy and transfer momentum.

"Field lines" or "lines of force" are a visualization tool suitable for drawing vector fields. They are maps of the fields and the fields are real things. Is that good enough for you?

And, yes, the electromagnetic interaction can be described in another (more fundamental) way as exchange of bosons in a quantum field theory. But that does not change the fact they these fields store energy and transfer momentum.