# Deflection of current in a metal plate conductor

If I have a metal plate (square in shape) and an electric current moves from one side to the other. I understand that most of the current will take the path of least resistance but all paths will be taken. However, is it possible to use magnets to control the direction of the current by deflecting electrons via the Lorentz force. For example, could I concentrate more current to take the path of least resistance and reduce the spreading. Or could I force more current to one side of the path rather than the other. Thanks.

The phrase "current takes the path of least resistance" has done a lot of harm in education, I think, and still it persists.

At face value, it implies that, even in a medium of nearly uniform resistance (for any particular path current might take through it), there is always and only one exclusive well-worn path that current flows down, and nothing elsewhere.

This is clearly contradicted by the total resistance going down when we connect resistors in parallel, for example. The total resistance is not simply the one lowest value.

It is much more useful to say "current prioritizes lower resistance", or that it distributes according to relative resistance along the path.

It's not clear if this has caused you any confusion, but I just want to head off this problematic phrase sooner than later, and to better inform readers.

As for moving currents with magnetic fields; certainly! Within a conductor, this gives the Hall effect: for current flowing uniformly across a sheet for example, there should normally be zero voltage across its width -- current is uniform after all. All the voltage drop is lengthwise, parallel to the current flow. If we apply a magnetic field through the plate, the current path is bent to one side, and more charge "piles up" on one side than the other -- the electric field is no longer parallel to the axis of current flow, but is skewed at an angle.

How much angle, depends on the density of charge carriers in the conductor. It's normally a very slight effect in metals: there are so many electrons present, that their average (drift) motion due to any realistic current flow is negligible, and therefore the deflection is small. We usually use semiconductors to demonstrate the Hall effect: with fewer charge carriers, drift velocity is higher, and so too the deflection. Indeed it's large enough we can construct even quite tiny integrated circuits, with a Hall device and amplifier together, to sense rather modest magnetic fields, such as the current flow through a wire.

is it possible to use magnets to control the direction of the current by deflecting electrons via the Lorentz force.

Yes. This is how Hall Effect sensors work. Current flows from one edge of a square to its opposite edge. If a magnetic field is present, the electrons are deflected from a straight path from one side of the square to the other, and create a (very small) voltage difference between two remaining sides of the square.

The voltage created is very small, so I don't know how practical it would be for you to create such a Hall Effect sensor yourself. You would need a very low noise amplifier to get a useful signal.

• It's really difficult to measure in metals, I once tried it with a 5.5-digit meter with ~µV resolution but didn't see anything. But I think it should still be doable with patience using correct probing technique and signal conditioning - since physicists from ancient time discovered that using only Wheatstone bridges (well-made ones can be incredibly sensitive, down to several parts per million), and today's tech should only make it easier - but it's why physics classes usually use semiconductors to demonstrate this effect, which is much greater. Apr 20 at 2:38

In the question it is not clear how the electromotive force is applied to the two opposite ends of the plate, i.e. is it applied between two points on the opposite faces or is each face at constant (distributed) potential? The current distribution in the plate will follow the lines of force of the electric field. In the central part of the plate, however, we can affirm a certain uniformity of the lines of force of the field. By adding an external magnetic field orthogonal to the plate, we will have different paths depending on the case. A resultant force of the two forces will act on the charges: the Culombian and the Lorentz forces,that is: F= q(E+v × B) and the current will follow a curl path if the induction B is very intense.