The diagram above demonstrates the Lorentz force, Yet I wonder… must there be two magnets/electromagnets?
If the two magnets form a magnetic field of $1$ $Tesla$ acting on the wire, why not use 1 magnet and make the wire really really close to it. So that the gap would be 0. Will $B$ still be valid based on one magnet?
Best Answer
Let us take a bar magnet and place a current carrying wire very close to it as shown below
The magnetic field in that region of space( very close to the wire and thus the magnet ) can be treated as a uniform field( approximately ).
Now, the charges within the current carrying wire experience a Lorentz force given by
$$\vec{F} = q(\vec{v}\times\vec{B}) + q\vec{E}$$
Let us see how
Consider an electron moving within the wire. This electron would experience an electric force due to the presence of an electric field inside the wire and a magnetic force due to the magnetic field created by the magnet outside the wire. So, you need not have two magnets to produce a Lorentz force. However, having two magnets would enhance the strength of the magnetic field and thus the magnetic force. Also, having two magnets would better ensure the presence of a uniform magnetic field unlike in the case of a single magnet. I conclude by saying that Lorentz force will act on the charged particle even in the presence of a single magnet because all we need is an electric field and a magnetic field( which is created by a single magnet ).
Also, you need not place the wire close to the magnet. You can place it at a considerable distance from the single magnet. In this case, you will have a non-uniform magnetic field in space. Nevertheless, a Lorentz force will continue to act on the charged particles within the current carrying wire( the magnetic force will vary from point to point ).