# A positive charge moves towards a wire with positive current. How are the effects of the magnetic field explained upon a Lorentz transformation?

Consider a positive charge $P$ moving towards a wire that has the same density of positive charges and negative charges, but so that the positive charges are moving to the right. Then the magnetic field should cause $P$ to move to the left.

Now consider the Lorentz transformation that makes $P$ still. Now the wire is moving to approach $P$. But because $P$ is still, it cannot be affected by any magnetic effects, so any force on it is caused by electric effects.

So now we have a wire with positive charges moving to the right approaching $P$, and somehow this creates an electric force on $P$ to move to the left. How?

• Related, but different, configuration discussed in this Physics SE question. Thus this question shall be not marked as duplicate, I reckon. – user154997 Oct 2 '17 at 9:37
• I was sure I had seen it before: you can deduce the answer from this Physics SE answer. – user154997 Oct 2 '17 at 14:21

Consider a positive charge P moving towards a wire that has the same density of positive charges and negative charges, but so that the positive charges are moving to the right.

That scenario is not unphysical. But it is not a common everyday situation either.

So something special happens: Charge P does not veer to the left or to the right, it moves straight towards the wire. The motion of P does not indicate an existence of a magnetic field.

Now consider the Lorentz transformation that makes P still. Now the wire is moving to approach P. But because P is still, it cannot be affected by any magnetic effects, so any force on it is caused by electric effects.

Yes. Particle P does not feel any force to any direction.

One single wire with electric current has that kind of magnetic field around it that a particle moving towards it does not feel a Lorentz-force. A rectangular circuit with electric current has a different kind of magnetic field around it: That magnetic field is a sum of four single-wire magnetic fields. The usual rules of magnetism apply to the latter magnetic field.

• I changed my mind. All of the above wrong. – stuffu Nov 29 '17 at 20:51