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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:

enter image description here

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>

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    $\begingroup$ "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. $\endgroup$ – probably_someone Apr 18 '18 at 16:35
  • $\begingroup$ @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? $\endgroup$ – sangstar Apr 18 '18 at 21:45
  • $\begingroup$ 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. $\endgroup$ – probably_someone Apr 18 '18 at 21:49
  • $\begingroup$ I was not aware of this, which I'm surprised by. Cheers! $\endgroup$ – sangstar Apr 18 '18 at 21:52
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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.

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  • $\begingroup$ "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. $\endgroup$ – Aaron Stevens Aug 2 '18 at 16:06

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